25-chuyên-đề-Toán-Tiểu-học

["12 \u2013 4 = 8 (lit) L\u01b0\u1ee3ng n\u01b0\u1edbc th\u00f9ng III ban \u0111\u1ea7u l\u00e0: 9 x 3 \u2013 (12 + 8) = 7 (l\u00edt) \u0110\u00e1p s\u1ed1: I: 12 l\u00edt ; II: 8 l\u00edt ; III: 7 l\u00edt 24.TO\u00c1N C\u1ed4 40 B\u00c0I TO\u00c1N C\u1ed4 NGUY\u1ec4N NG\u1eccC THI\u00caN TRANG ( Ph\u00fa Y\u00ean) M\u1eddi qu\u00fd th\u1ea7y c\u00f4, c\u00e1c b\u1ea1n c\u00f9ng gi\u1ea3i b\u00e0i v\u00e0 g\u1edfi cho [email protected]. C\u00e1m \u01a1n. B\u00e0i 1 M\u1ed9t anh ch\u00e0ng \u0111i c\u00e2u c\u00e1. Khi tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi:\\\" Anh c\u00e2u \u0111\u01b0\u1ee3c bao nhi\u00eau c\u00e1?\\\", anh ta n\u00f3i:\\\" M\u1ed9t n\u1eefa c\u1ee7a 8, s\u1ed1 6 kh\u00f4ng c\u00f3 \u0111\u1ea7u, s\u1ed1 ch\u00edn kh\u00f4ng c\u00f3 \u0111u\u00f4i\\\" H\u1ecfi anh ch\u00e0ng \u0111\u00e3 c\u00e2u \u0111\u01b0\u1ee3c bao nhi\u00eau c\u00e1. B\u00e0i 2 Ng\u01b0\u1eddi ta h\u1ecfi m\u1ed9t \u00f4ng gi\u00e0 r\u1eb1ng \u00f4ng \u0111\u00e3 tham gia qu\u00e2n \u0111\u1ed9i trong bao l\u00e2u, \u00f4ng tr\u1ea3 l\u1eddi:S\u1ed1 n\u0103m tham gia qu\u00e2n \u0111\u1ed9i c\u1ee7a t\u00f4i b\u1eb1ng 1\/27 tu\u1ed5i c\u1ee7a t\u00f4i hay b\u1eb1ng 1\/7 tu\u1ed5i c\u1ee7a ch\u00e1u t\u00f4i ho\u1eb7c b\u1eb1ng \u0111\u00fang tu\u1ed5i c\u1ee7a con trai t\u00f4i. Ngo\u00e0i ra tu\u1ed5i c\u1ee7a t\u00f4i g\u1ea7n s\u1ed1 90 h\u01a1n l\u00e0 g\u1ea7n s\u1ed1 100. H\u1ecfi \u00f4ng gi\u00e0 \u0111\u00e3 tham gia qu\u00e2n \u0111\u1ed9i trong bao l\u00e2u? B\u00e0i 3 Ba ng\u01b0\u1eddi b\u1ea1n \u0103n trong 1 c\u00e1i qu\u00e1n, cu\u1ed1i b\u1eefa \u0103n s\u1ed1 ti\u1ec1n c\u1ea7n ph\u1ea3i tr\u1ea3 l\u00e0 25 \u0111\u1ed3ng. M\u1ed7i ng\u01b0\u1eddi b\u1ecf ra 10 \u0111\u1ed3ng, ch\u1ee7 qu\u00e1n tr\u1ea3 lai cho h\u1ecd ba t\u1edd 1 \u0111\u1ed3ng v\u00e0 1 t\u1edd 2 \u0111\u1ed3ng. M\u1ed5i ng\u01b0\u1eddi l\u1ea5y v\u1ec1 t\u1edd 1 \u0111\u1ed3ng, c\u00f2n t\u1edd 2 \u0111\u1ed3ng h\u1ecd kh\u00f4ng chia. K\u1ebft qu\u1ea3 l\u00e0 m\u1ed7i ng\u01b0\u1eddi ph\u1ea3i thanh to\u00e1n 9 \u0111\u1ed3ng. Ta th\u1ea5y 9*3=27 (\u0111\u1ed3ng). N\u1ebfu t\u00ednh c\u1ea3 2 \u0111\u1ed3ng c\u00f2n l\u1ea1i th\u00ec t\u1ea5t c\u1ea3 l\u00e0 29 \u0111\u1ed3ng. V\u1eady c n 1 \u0111\u1ed3ng m\u1ea5t \u0111i \u0111\u00e2u? B\u00e0i 4 B\u1ed1n c\u00e1i ch\u00e9n v\u00e0 1 c\u00e1i \u1ea5m n\u1eb7ng b\u1eb1ng 17 th\u1ecfi ch\u00ec. Ri\u00eang c\u00e1i \u1ea5m n\u1eb7ng b\u1eb1ng 1 c\u00e1i ch\u00e9n v\u00e0 7 th\u1ecfi ch\u00ec. H\u1ecfi c\u00e1i \u1ea5m c\u00e2n n\u1eb7ng b\u1eb1ng m\u1ea5y th\u1ecfi ch\u00ec? B\u00e0i 5 Khi ng\u01b0\u1eddi ta h\u1ecfi con c\u00e1 b\u1eaft \u0111\u01b0\u1ee3c n\u1eb7ng bao nhi\u00eau , ng\u01b0\u1eddi \u0111\u00e1nh c\u00e1 tr\u1ea3 l\u1eddi :\\\" \u0110u\u00f4i n\u00f3 n\u1eb7ng 150g, \u0111\u1ea7u n\u00f3 n\u1eb7ng b\u1eb1ng \u0111u\u00f4i v\u00e0 1\/2 th\u00e2n, c n th\u00e2n n\u1eb7ng b\u1eb1ng \u0111\u1ea7u v\u00e0 \u0111u\u00f4i.\\\" Nh\u01b0 th\u1ebf con c\u00e1 c\u1ee7a anh ta n\u1eb7ng bao nhi\u00eau?","B\u00e0i 6 M\u1ed9t l\u00e0ng \u1edf v\u00f9ng cao n\u1ecd n\u1ed5i ti\u1ebfng v\u1ec1 nhi\u1ec1u ng\u01b0\u1eddi s\u1ed1ng l\u00e2u. Ng\u01b0\u1eddi ta \u0111\u1eb7c bi\u1ec7t t\u00f4n k\u00ednh c\u1ee5 gi\u00e0 I-s\u01a1-khan, ng\u1eeb\u01a1i \u0111\u00e3 c\u00f3 con, ch\u00e1u, ch\u1eaft, ch\u00edt. T\u1ed5ng c\u1ed9ng t\u1ea5t c\u1ea3 c\u00f9ng v\u1edbi c\u1ee5 2801 ng\u01b0\u1ee3i.Ch\u00edt c\u1ee7a c\u1ee5 nh\u1ecf v\u00e0 ch\u01b0a c\u00f3 con, ngo\u00e0i ra t\u1ea5t c\u1ea3 \u0111\u1ec1u c\u00f3 s\u1ed1 con nh\u01b0 nhau, c\u00e1c con h\u1ecd \u0111\u1ec1u kho\u1ebb m\u1ea1nh. H\u1ecfi nh\u01b0 v\u1eady c\u1ee5 I-s\u01a1-khan c\u00f3 bao nhi\u00eau ng\u01b0\u1eddi con. B\u00e0i 7 B\u1ed1n gia \u0111\u00ecnh mang h\u1ecd Smith, Braun, Jonhson v\u00e0 Robinson c\u00f3 t\u1ea5t c\u1ea3 8 ng\u01b0\u1eddi con. M\u1ed7i gia \u0111\u00ecnh c\u00f3 1 trai, 1 g\u00e1i. M\u1ed7i l\u1ea7n ng\u01b0\u1eddi ta cho l\u0169 tr\u1ebb 32 qu\u1ea3 t\u00e1o. Anna \u0111\u01b0\u1ee3c 1 qu\u1ea3 ,Betti \u0111\u01b0\u1ee3c 2 qu\u1ea3, Daisy 3 qu\u1ea3 v\u00e0 Mary 4 qu\u1ea3. Th\u1ebf nh\u01b0ng Tom Raul \u0111\u01b0\u1ee3c s\u1ed1 t\u00e1o g\u1ea5p 2 l\u1ea7n ch\u1ecb n\u00f3; Gary Smith v\u00e0 ch\u1ecb n\u00f3 \u0111\u01b0\u1ee3c s\u1ed1 t\u00e1o b\u1eb1ng nhau; Ben Johnson \u0111\u01b0\u1ee3c s\u1ed1 t\u00e1o g\u1ea5p 3 l\u1ea7n ch\u1ecb n\u00f3 v\u00e0 Dick Robinson \u0111\u01b0\u1ee3c s\u1ed1 t\u00e1o g\u1ea5p 4 l\u1ea7n ch\u1ecb n\u00f3. H\u00e3y x\u00e1c \u0111\u1ecbnh h\u1ecd c\u1ee7a c\u00e1c c\u00f4 con g\u00e1i B\u00e0i 8 Ba anh em trai Pi-e, P\u00f4n v\u00e0 Gi\u1eafc l\u1ea5y v\u1ee3 v\u00e0 s\u1ed1ng \u1edf c\u00e1c th\u00e0nh ph\u1ed1 kh\u00e1c nhau, h\u1ecd \u00edt khi g\u1eb7p nhau. Trong m\u1ed9t k\u00ec ngh\u1ec9 h\u1ecd quy\u1ebft \u0111\u1ecbnh t\u1ee5 h\u1ecdp c\u00f9ng v\u1edbi t\u1ea5t c\u1ea3 con c\u00e1i c\u1ee7a h\u1ecd. Nh\u1eefng \u0111\u1ee9 tr\u1ebb nhanh ch\u00f3ng vui v\u1ebb v\u00e0 th\u00e2n m\u1eadt v\u1edbi nhau. \u00d4ng b\u1ea1n gi\u00e0 c\u1ee7a c\u1ea3 ba ng\u01b0\u1eddi l\u00e0 Me-men t\u1edbi ch\u01a1i mu\u1ed1n bi\u1ebft \u0111\u1ee9a b\u00e9 n\u00e0o l\u00e0 con c\u1ee7a ai, sau khi h\u1ecfi \u00f4ng nh\u1eadn \u0111\u01b0\u1ee3c c\u00e1c c\u00e2u tr\u1ea3 l\u1eddi sau: 1. I-da-ben-la: Ch\u00e1u nhi\u1ec1u h\u01a1n Gian 3 tu\u1ed5i 2. T\u00ea-r\u00ea-da: Cha ch\u00e1u l\u00e0 Gi\u1eafc 3. E-chi\u00ean: Ch\u00e1u \u00edt h\u01a1n I-da-ben-la 2 tu\u1ed5i. 4. Mary: Ch\u00e1u th\u00edch ch\u01a1i v\u1edbi anh em con ch\u00fa con b\u00e1c h\u01a1n l\u00e0 ch\u01a1i v\u1edbi anh c\u1ee7a ch\u00e1u. 5. Ka-rin: Ch\u00e1u l\u00e0 con g\u00e1i c\u1ee7a b\u1ed1 Pi-e 6. An-na: T\u1ed1t h\u01a1n h\u1ebft h\u00e3y ch\u1ea1y ra xa c\u00f9ng v\u1edbi c\u00e1c con trai c\u1ee7a b\u00e1c Gi\u1eafc 7. Gian: Cha ch\u00e1u c\u0169ng nh\u01b0 anh em c\u1ee7a cha \u0111\u1ec1u c\u00f3 \u00edt h\u01a1n 4 ng\u01b0\u1eddi con. 8. Fr\u0103ng-xoa: Cha ch\u00e1u c\u00f3 \u00edt con h\u01a1n t\u1ea5t c\u1ea3. Kh\u00f4ng h\u1ecfi th\u00eam g\u00ec c\u1ea3, c\u1ee5 Me-men \u0111\u00e3 bi\u1ebft \u0111\u1ee9a tr\u1ebb n\u00e0o l\u00e0 con c\u1ee7a ai. B\u1ea1n h\u00e3y cho bi\u1ebft c\u1ee5 suy lu\u1eadn nh\u01b0 th\u1ebf n\u00e0o. B\u00e0i 9 C\u00f3 m\u1ed9t \u00f4ng vua gi\u00e0 kh\u00f4ng c\u00f3 ng\u01b0\u1eddi k\u1ebf v\u1ecb. Th\u1ea5y m\u00ecnh kh\u00f4ng c\u00f2n s\u1ed1ng \u0111\u01b0\u1ee3c bao l\u00e2u n\u1eefa, \u00d4ng quy\u1ebft \u0111\u1ecbnh m\u1edf cu\u1ed9c thi ch\u1ecdn Th\u00e1i t\u1eed c\u00f3 n\u0103ng l\u1ef1c. C\u00f3 4 ch\u00e0ng trai t\u00e0i gi\u1ecfi nh\u1ea5t v\u01b0\u01a1ng qu\u1ed1c t\u1edbi tham d\u1ef1. Nh\u00e0 vua ti\u1ebfn h\u00e0nh ch\u1ecdn nh\u01b0 sau: -\u00d4ng b\u1ecbt m\u1eaft b\u1ed1n ch\u00e0ng trai v\u00e0 x\u1ebfp h\u1ecd ng\u1ed1i v\u00e0o b\u00e0n tr\u00f2n. Nh\u00e0 vua n\u00f3i: \\\" Ta s\u1ebd \u0111\u1eb7t l\u00ean \u0111\u1ea7u m\u1ed7i ng\u01b0\u1eddi m\u1ed9t m\u0169 mi\u1ec7ng v\u00e0ng ho\u1eb7c b\u1ea1c. Khi b\u1ecf kh\u0103n b\u1ecbt m\u1eaft ra, ai nh\u00ecn th\u1ea5y s\u1ed1 mi\u1ec7n v\u00e0ng nhi\u1ec1u h\u01a1n mi\u1ec7n b\u1ea1c th\u00ec \u0111\u1ee9ng l\u00ean v\u00e0 \u0111\u1ee9ng \u0111\u00f3 cho \u0111\u1ebfn khi c\u00f3 ng\u01b0\u1eddi n\u00f3i \u0111\u01b0\u1ee3c tr\u00ean \u0111\u1ea7u m\u00ecnh m\u0169 mi\u1ec7n m\u00e0u g\u00ec. Ai n\u00f3i \u0111\u01b0\u1ee3c s\u1ebd l\u00e0 ng\u01b0\u1eddi k\u1ebf v\u1ecb ta. Kh\u0103n b\u1ecbt m\u1eb7t \u0111\u01b0\u1ee3c b\u1ecf ra, c\u00e1c ch\u00e0ng trai nh\u00ecn nhau v\u00e0 \u0111\u1ec1u \u0111\u1ee9ng l\u00ean. Sau m\u1ed9t h\u1ed3i, m\u1ed9t ng\u01b0\u1eddi k\u00eau l\u00ean: -Th\u01b0a \u0111\u1ebf v\u01b0\u01a1ng, tr\u00ean \u0111\u1ea7u con l\u00e0 mi\u1ec7ng v\u00e0ng Anh ta \u0111\u00e3 suy \u0111o\u00e1n \u0111\u00fang. V\u1eady nh\u00e0 vua \u0111\u00e3 \u0111\u1eb7t m\u0169 mi\u1ec7ng g\u00ec l\u00ean \u0111\u1ea7u c\u00e1c ch\u00e0ng trai v\u00e0 ch\u00e0ng trai th\u00f4ng minh \u0111\u00f3 \u0111\u00e3 suy lu\u1eadn nh\u01b0 th\u1ebf n\u00e0o? B\u00e0i 10 T\u00f4i ch\u01a1i c\u1edd c\u0169ng kh\u00e1 nh\u01b0ng hai ng\u1eeb\u01a1i b\u1ea1n th\u00e2n c\u1ee7a t\u00f4i l\u00e0 nh\u1eefng tay c\u1edd tuy\u1ec7t di\u1ec7u. T\u00f4i ch\u01a1i v\u1edbi m\u1ed7i ng\u1eeb\u01a1i m\u1ed9t v\u00e1n v\u00e0 c\u1ea3 hai \u0111\u1ec1u th\u1eafng t\u00f4i d\u1ec5 d\u00e0ng. M\u1ed9t ng\u01b0\u1eddi b\u1ea1n nh\u1ecf c\u1ee7a t\u00f4i- m\u1edbi 10 tu\u1ed5i v\u00e0 ch\u1ec9 bi\u1ebft c\u00e1ch ch\u01a1i c\u1edd nh\u01b0ng l\u1ea1i c\u1ea3 quy\u1ebft l\u00e0 s\u1ebd ch\u01a1i t\u1ed1t h\u01a1n t\u00f4i.\u0110\u1ec3 ch\u1ee9ng t\u1ecf c\u1eadu ta ra \u0111i\u1ec1u ki\u1ec7n : \\\" Ch\u00e1u s\u1ebd ch\u01a1i c\u00f9ng m\u1ed9t l\u00fac v\u1edbi c\u1ea3 hai ng\u01b0\u1eddi b\u1ea1n c\u1ee7a ch\u00fa v\u00e0 ch\u1eafc ch\u1eafn l\u00e0 s\u1ebd \u0111\u1ea1t k\u1ebft qu\u1ea3 t\u1ed1t h\u01a1n ch\u00fa l\u00e0 kh\u00f4ng thua c\u1ea3 hai ng\u01b0\u1eddi.\\\" C\u00f3 th\u1ec3 l\u00fd gi\u1ea3i s\u1ef1 th\u00e0nh c\u00f4ng c\u1ee7a ng\u01b0\u1eddi b\u1ea1n nh\u1ecf nh\u01b0 th\u1ebf n\u00e0o.","B\u00e0i 11 M\u1ed9t b\u00e0 n\u00f4ng d\u00e2n mang hai gi\u1ecf tr\u1ee9ng ra ch\u1ee3 b\u00e1n, m\u1ed7i gi\u1ecf c\u00f3 30 tr\u1ee9ng. Trong gi\u1ecf tr\u1ee9ng b\u00e9 , b\u00e0 d\u1ef1 \u0111\u1ecbnh s\u1ebd b\u00e1n v\u1edbi gi\u00e1 1 \u0111\u1ed3ng \u0111\u01b0\u1ee3c 3 qu\u1ea3. Gi\u1ecf tr\u1ee9ng to b\u00e0n s\u1ebd b\u00e1n 1 \u0111\u1ed3ng 2 qu\u1ea3. Tuy nhi\u00ean khi \u1edf ch\u1ee3 b\u00e0 thay \u0111\u1ed5i \u00fd \u0111\u1ecbnh, b\u00e0 \u0111\u1ec3 tr\u1ee9ng l n l\u1ed9n v\u00e0 b\u00e1n v\u1edbi gi\u00e1 2 \u0111\u1ed3ng \u0111\u01b0\u1ee3c 5 qu\u1ea3. Nh\u01b0 th\u1ebf c\u00f3 l\u1ee3i cho b\u00e0 so v\u1edbi \u00fd \u0111\u1ecbnh ban \u0111\u1ea7u kh\u00f4ng? B\u00e0i 12 Hai ng\u01b0\u1eddi b\u1ea1n g\u1eb7p nhau. M\u1ed9t ng\u01b0\u1eddi h\u1ecfi b\u1ea1n m\u00ecnh :\\\" C\u00e1c con c\u1ee7a anh bao nhi\u00eau tu\u1ed5i?\\\" Ng\u01b0\u1eddi th\u1ee9 hai tr\u1ea3 l\u1eddi: \\\"T\u00f4i c\u00f3 hai \u0111\u1ee9a con trai : tu\u1ed5i t\u00f4i g\u1ea5p 4 l\u1ea7n tu\u1ed5i \u0111\u1ee9a th\u1ee9 nh\u1ea5t v\u00e0 g\u1ea5p 7 l\u1ea7n \u0111\u1ee9a th\u1ee9 hai\\\". H\u1ecfi \u00f4ng b\u1ed1 bao nhi\u00eau tu\u1ed5i v\u00e0 c\u00e1c con c\u1ee7a \u00f4ng bao nhi\u00eau tu\u1ed5i on g\u00e0 c\u00e1ch 1 ng\u00e0y \u0111\u1ebb 1 tr\u1ee9ng, con th\u1ee9 2 c\u00e1ch 3 ng\u00e0y \u0111\u1ebb 1 tr\u1ee9ng , con th\u1ee9 3 c\u00e1ch 4 ng\u00e0y \u0111\u1ebb 1 tr\u1ee9ng, v\u00e0 con th\u1ee9 4 c\u00e1ch 7 ng\u00e0y \u0111\u1ebb 1 tr\u1ee9ng. M\u1ed9t l\u1ea7n c\u00f4 Mari l\u1ea5y trong chu\u1ed3ng \u0111\u01b0\u1ee3c 4 qu\u1ea3 tr\u1ee9ng v\u00e0 khoe v\u1edbi b\u00e0 h\u00e0ng x\u00f3m. B\u00e0 ta ch\u00fac m\u1eebng c\u00f4 v\u00e0 h\u1ecfi: S\u1ed1 ng\u00e0y ng\u1eafn nh\u1ea5t l\u00e0 m\u1ea5y ng\u00e0y (k\u1ec3 t B\u00e0i 13 C\u00f4 Mari c\u00f3 4 con g\u00e0 m\u00e1i. C\u00f4 nh\u1eadn th\u1ea5y r\u1eb1ng 1 c\u1eeb b\u00e2y gi\u1edd) \u0111\u1ec3 c\u00f4 c\u00f3 th\u1ec3 l\u1ea5y \u0111\u01b0\u1ee3c 4 tr\u1ee9ng n\u1eefa? B\u1ea1n h\u00e3y gi\u00fap c\u00f4 Mari B\u00e0i 14 M\u1ed9t c\u00f4 g\u00e1i mang ra ch\u1ee3 hai gi\u1ecf tr\u1ee9ng. B\u1ea5t ch\u1ee3t m\u1ed9t ch\u00fa b\u00e9 x\u00f4 v\u00e0o ng\u01b0\u1eddi , hai gi\u1ecf tr\u1ee9ng r\u01a1i , tr\u1ee9ng v\u1ee1. Ch\u00fa b\u00e9 xin l\u1ed7i c\u00f4 v\u00e0 h\u1ecfi c\u00f4 c\u00f3 t\u1ea5t c\u1ea3 bao nhi\u00eau tr\u1ee9ng \u0111\u1ec3 ch\u00fa \u0111\u1ec1n ti\u1ec1n , c\u00f4 g\u00e1i tr\u1ea3 l\u1eddi: \\\"Ch\u1ecb kh\u00f4ng \u0111\u1ebfm nh\u01b0ng khi x\u1ebfp v\u00e0o gi\u1ecf theo 2 qu\u1ea3 m\u1ed9t, ba qu\u1ea3 m\u1ed9t, 4 qu\u1ea3 m\u1ed9t, 5 qu\u1ea3 m\u1ed9t, 6 qu\u1ea3 m\u1ed9t l\u1ea7n n\u00e0o c\u0169ng d\u01b0 ra 1 qu\u1ea3. C\u00f2n khi x\u1ebfp theo 7 qu\u1ea3 th\u00ec kh\u00f4ng d\u01b0 qu\u1ea3 n\u00e0o H\u1ecfi trong hai gi\u1ecf c\u00f3 bao nhi\u00eau qu\u1ea3 tr\u1ee9ng B\u00e0i 15 Ng\u01b0\u1eddi ta \u0111\u1eb7t trong kho 6 th\u00f9ng r\u01b0\u1ee3u. T\u1eeb th\u00f9ng th\u1ee9 nh\u1ea5t \u0111\u1ebfn th\u00f9ng th\u1ee9 6 t\u01b0\u01a1ng \u1ee9ng ch\u1ee9a: 310 l\u00edt, 200 l\u00edt, 190 l\u00edt, 180 l\u00edt, 160 l\u00edt v\u00e0 150 l\u00edt. Ng\u00e0y th\u1ee9 nh\u1ea5t hai ng\u01b0\u1eddi mang r\u01b0\u1ee3u \u0111i b\u00e1n, ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t b\u00e1n \u0111\u01b0\u1ee3c 2 th\u00f9ng, ng\u01b0\u1eddi th\u1ee9 hai b\u00e1n \u0111\u01b0\u1ee3c 3 th\u00f9ng, h\u01a1n n\u1eefa ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t b\u00e1n \u0111\u01b0\u1ee3c s\u1ed1 r\u01b0\u1ee3u b\u1eb1ng m\u1ed9t n\u1eefa s\u1ed1 r\u01b0\u1ee3u ng\u01b0\u1eddi th\u1ee9 hai \u0111\u00e3 b\u00e1n. H\u1ecfi th\u00f9ng r\u01b0\u1ee3u n\u00e0o c\u00f2n trong kho B\u00e0i 16 Tr\u1ea3 l\u1eddi v\u1ec1 tu\u1ed5i c\u1ee7a m\u00ecnh, 1 ng\u01b0\u1eddi \u0111\u00e0n \u00f4ng n\u00f3i nh\u01b0 sau: \\\"C\u1ee9 v\u00e0o sinh nh\u1eadt c\u1ee7a t\u00f4i, cha t\u00f4i l\u1ea1i gi\u1ebft 1 con c\u1eebu \u0111\u1ec3 \u0103n m\u1eebng, b\u1ed9 da c\u1eebu \u00f4ng x\u1ebfp v\u00e0o 1 ch\u1ed7. T\u00f4i l\u1edbn l\u00ean l\u1ea5y v\u1ee3 c\u0169ng sinh \u0111\u01b0\u1ee3c 1 th\u1eb1ng con trai, v\u00e0o sinh nh\u1eadt n\u00e0o c\u1ee7a n\u00f3 t\u00f4i c\u0169ng l\u1ea1i gi\u1ebft c\u1eebu, c\u1ea5t b\u1ed9 da v\u00e0o 1 ch\u1ed7. N\u0103m nay s\u1ed1 da c\u1eebu c\u1ee7a t\u00f4i b\u1eb1ng s\u1ed1 da c\u1eebu c\u1ee7a n\u00f3. H\u1ecfi tu\u1ed5i ng\u01b0\u1eddi \u0111\u00e0n \u00f4ng v\u00e0 con trai c\u1ee7a \u00f4ng ta l\u00e0 bao nhi\u00eau? B\u00e0i 17 Ba ng\u01b0\u1eddi b\u1ea1n r\u1ea5t th\u00edch \u0111i b\u01a1i. Ng\u01b0\u1eddi th\u1ee9i nh\u1ea5t luy\u1ec7n t\u1eadp t\u1ea1i b\u1ec3 b\u01a1i ba ng\u00e0y 1 l\u00e2n, Ng\u01b0\u1eddi th\u1ee9 2 th\u00ec 4 ng\u00e0y 1 l\u1ea7n. Ng\u01b0\u1eddi th\u1ee9 3 n\u0103m ng\u00e0y 1 l\u1ea7n. T\u00ecm s\u1ed1 ng\u00e0y l\u1edbn nh\u1ea5t m\u00e0 h\u1ecd c\u00f3 th\u1ec3 c\u00f9ng nhau \u0111i d\u1ea1o ch\u01a1i. B\u00e0i 18 Ba ng\u01b0\u1eddi \u0111\u00e0n \u00f4ng v\u00e0 2 ch\u00fa b\u00e9 ph\u1ea3i qua 1 con s\u00f4ng. H\u1ecd c\u00f3 1 con thuy\u1ec1n nh\u01b0ng ch\u1ec9 ch\u1edf \u0111\u01b0\u1ee3c 1 ng\u01b0\u1eddi \u0111\u00e0n \u00f4ng ho\u1eb7c 2 ch\u00fa b\u00e9. T\u1ea5t c\u1ea3 h\u1ecd \u0111\u00e3 qua s\u00f4ng nh\u01b0 th\u1ebf n\u00e0o. N\u1ebfu","chi\u1ec1u r\u1ed9ng l\u00e0 100 m th\u00ec qu\u00e3ng \u0111\u01b0\u1eddng m\u00e0 thuy\u1ec1n ph\u1ea3i \u0111i l\u00e0 bao nhi\u00eau m\u00e9t? B\u00e0i 19 B\u1ed1 m\u1eb9 v\u00e0 hai c\u1eadu con trai c\u1ea7n ph\u1ea3i qua s\u00f4ng b\u1eb1ng 1 con thuy\u1ec1n. B\u1ed1 v\u00e0 m\u1eb9 m\u1ed7i ng\u01b0\u1eddi n\u1eb7ng 70 kg, m\u1ed7i ng\u01b0\u1eddi con n\u1eb7ng 35 kg. H\u1ecd l\u00e0m th\u1ebf n\u00e0o \u0111\u1ec3 qua s\u00f4ng n\u1ebfu thuy\u1ec1n ch\u1ec9 ch\u1edf \u0111\u1ebfn 70 kg. L\u01b0u \u00fd l\u00e0 m\u1ed7i ng\u01b0\u1eddi \u0111\u1ec1u bi\u1ebft ch\u00e8o thuy\u1ec1n. B\u00e0i 20 C\u00f3 2 c\u00e1i th\u00f9ng: m\u1ed9t th\u00f9ng r\u01b0\u1ee3u c\u00f2n th\u00f9ng kia l\u00e0 th\u00f9ng n\u01b0\u1edbc, l\u01b0\u1ee3ng n\u01b0\u1edbc v\u00e0 r\u01b0\u1ee3u ngang nhau. T\u1eeb th\u00f9ng r\u01b0\u1ee3u ng\u01b0\u1eddi ta l\u1ea5y ra 1 l\u00edt r\u01b0\u1ee3u r\u00f3t v\u00e0o th\u00f9ng n\u01b0\u1edbc. Sau \u0111\u00f3 l\u1ea1i \u0111\u1ed7 1 l\u00edt r\u01b0\u1ee3u n\u01b0\u1edbc t\u1ea1o th\u00e0nh v\u00e0o l\u1ea1i th\u00f9ng r\u01b0\u1ee3u. H\u1ecfi ph\u1ea7n n\u01b0\u1edbc trong th\u00f9ng r\u01b0\u1ee3u v\u00e0 ph\u1ea7n r\u01b0\u1ee3u trong th\u00f9ng n\u01b0\u1edbc, ph\u1ea7n n\u00e0o l\u1edbn h\u01a1n. B\u00e0i 21: Ba ng\u01b0\u1eddi c\u00f3 t\u00ean l\u00e0 A, B, C c\u00f9ng \u1edf trong 1 bu\u1ed3ng c\u1ee7a toa xe l\u1eeda . Trong khi tr\u00f2 chuy\u1ec7n m\u1edbi bi\u1ebft r\u1eb1ng: - N\u1ebfu \u0111\u1ed5i ch\u1ed7 c\u00e1c ch\u1eef s\u1ed1 trong tu\u1ed5i c\u1ee7a A th\u00ec \u0111\u01b0\u1ee3c tu\u1ed5i c\u1ee7a B - Hi\u1ec7u c\u1ee7a tu\u1ed5i gi\u1eefa A v\u00e0 B g\u1ea5p \u0111\u00f4i s\u1ed1 tu\u1ed5i c\u1ee7a C - Tu\u1ed5i c\u1ee7a B g\u1ea5p 10 l\u1ea7n tu\u1ed5i c\u1ee7a C H\u1ecfi m\u1ed7i ng\u01b0\u1eddi bao nhi\u00eau tu\u1ed5i. B\u00e0i 22: M\u1ed9t ng\u01b0\u1eddi n\u00f4ng d\u00e2n \u0111\u1ebfn g\u1eb7p nh\u00e0 vua v\u00e0 kh\u1ea9n c\u1ea7u : -\\\" K\u00ednh mong ho\u00e0ng \u0111\u1ebf t\u1ed1i cao, ng\u00e0i h\u00e3y cho k\u1ebb h\u1ea1 th\u1ea7n n\u00e0y xin 1 qu\u1ea3 t\u00e1o trong v\u01b0\u1eddn c\u1ee7a ng\u00e0i\\\". Nh\u00e0 vua ch\u1ea5p nh\u1eadn. Ng\u1eeb\u01a1i n\u00f4ng d\u00e2n \u0111i v\u00e0o v\u01b0\u1eddn v\u00e0 th\u1ea5y: To\u00e0n b\u1ed9 v\u01b0\u1eddn c\u1ee7a nh\u00e0 vua \u0111\u01b0\u1ee3c r\u00e0o b\u1eb1ng ba l\u1edbp. M\u1ed7i l\u1edbp r\u00e0o ch\u1ec9 c\u00f3 1 c\u1ed5ng ra v\u00e0o v\u00e0 c\u1ea1nh m\u1ed7i c\u1ed5ng ra v\u00e0o l\u00e0 1 ng\u01b0\u1eddi l\u00ednh g\u00e1c . Anh ta \u0111\u1ebfn g\u1eb7p ng\u01b0\u1eddi l\u00ednh g\u00e1c v\u00e0 n\u00f3i: -\\\"Nh\u00e0 vua \u0111\u1ed3ng \u00fd cho t\u00f4i l\u1ea5y 1 qu\u1ea3 t\u00e1o\\\". -\\\"Anh c\u1ee9 v\u00e0o l\u1ea5y nh\u01b0ng khi ra anh ph\u1ea3i \u0111\u01b0a t\u00f4i m\u1ed9t n\u1eefa s\u1ed1 t\u00e1o l\u1ea5y d\u01b0\u1ee3c v\u00e0 th\u00eam 1 qu\u1ea3\\\".Ng\u01b0\u1eddi l\u00ednh g\u00e1c th\u1ee9 nh\u1ea5t n\u00f3i. L\u1eddi n\u00f3i \u0111\u00f3 \u0111\u01b0\u1ee3c l\u1eb7p l\u1ea1i cho \u0111\u1ebfn khi g\u1eb7p ng\u01b0\u1eddi \u00ednh g\u00e1c th\u1ee9 hai v\u00e0 th\u1ee9 ba. H\u1ed3i x\u01b0a c\u0169ng c\u00f3 tham nh\u0169ng \u0111\u00f3 nha:01 :01 :p :p H\u1ecfi ng\u1eeb\u01a1i n\u00f4ng d\u00e2n ph\u1ea3i l\u1ea5y bao nhi\u00eau qu\u1ea3 \u0111\u1ec3 khi ra kh\u1ecfi l\u1edbp r\u00e0o anh ta ch\u1ec9 c n \u0111\u00fang 1 qu\u1ea3. B\u00e0i 23: M\u1ed9t b\u00e0 n\u00f4ng d\u00e2n mang 1 bao qu\u1ea3 l\u00ea ra ch\u1ee3 b\u00e1n. B\u00e0 b\u00e1n s\u1ed1 l\u00ea \u0111\u00f3 cho 6 ng\u01b0\u1eddi bu\u00f4n l\u00ea. B\u00e0 b\u00e1n cho ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t m\u1ed9t n\u1eefa s\u1ed1 l\u00ea v\u00e0 m\u1ed9t n\u1eefa qu\u1ea3 l\u00ea.ng\u1eeb\u01a1i th\u1ee9 2 m\u1ed9t n\u1eefa s\u1ed1 l\u00ea c\u00f2n l\u1ea1i v\u00e0 m\u1ed9t n\u1eefa qu\u1ea3 l\u00ea, ng\u01b0\u1eddi th\u1ee9 ba.....,ng\u01b0\u1eddi th\u1ee9 s\u00e1u m\u1ed9t n\u1eefa s\u1ed1 l\u00ea c\u00f2n l\u1ea1i v\u00e0 m\u1ed9t n\u1eefa qu\u1ea3 l\u00ea. B\u00e0 b\u00e1n h\u1ebft l\u00ea v\u00e0 m\u1ed7i ng\u1eeb\u01a1i trong 6 ng\u01b0\u1eddi \u0111\u00f3 mua \u0111\u01b0\u1ee3c s\u1ed1 l\u00ea nguy\u00ean qu\u1ea3. H\u1ecfi b\u00e0 n\u00f4ng d\u00e2n \u0111\u00e3 mang ra ch\u1ee3 bao nhi\u00eau qu\u1ea3 l\u00ea. B\u00e0i 24: M\u1ed9t ng\u1eeb\u01a1i ph\u1ee5 n\u1eef ra ch\u1ee3 b\u00e1n g\u00e0. Ng\u01b0\u1eddi kh\u00e1ch th\u1ee9 nh\u1ea5t \u0111i t\u1edbi mua m\u1ed9t n\u1eefa s\u1ed1 g\u00e0 v\u00e0 m\u1ed9t n\u1eefa con g\u00e0. Ng\u01b0\u1eddi kh\u00e1ch th\u1ee9 hai mua m\u1ed9t n\u1eefa s\u1ed1 g\u00e0 c\u00f2n l\u1ea1i v\u00e0 m\u1ed9t n\u1eefa con g\u00e0. Ng\u01b0\u1eddi th\u1ee9 ba \u0111\u1ebfn mua c\u0169ng v\u1eady. H\u1ecfi c\u00f4 ta mang ra ch\u1ee3 bao nhi\u00eau con g\u00e0, m\u1ed7i ng\u01b0\u1eddi mua \u0111\u01b0\u1ee3c bao nhi\u00eau con, n\u1ebfu s\u1ed1 g\u00e0 v\u1eeba h\u1ebft sau khi ng\u01b0\u1eddi th\u1ee9 ba \u0111i kh\u1ecfi. B\u00e0i 25: M\u1ed9t gi\u1ecf t\u00e1o \u0111\u01b0\u1ee3c l\u1ea5y \u0111i n qu\u1ea3 v\u00e0 1\/n s\u1ed1 qu\u1ea3 c\u00f2n l\u1ea1i. Sau \u0111\u00f3 ng\u1eeb\u01a1i ta l\u1ea5y \u0111i n qu\u1ea3 n\u1eefa. L\u00fac n\u00e0y s\u1ed1 t\u00e1o c\u00f2n l\u1ea1i trong gi\u1ecf \u0111\u00fang b\u1eb1ng m\u1ed9t n\u1eefa s\u1ed1 t\u00e1o ban \u0111\u1ea7u. H\u1ecfi ban \u0111\u1ea7u gi\u1ecf c\u00f3 nhi\u00eau qu\u1ea3 t\u00e1o? V\u1edbi s\u1ed1 t\u1ef1 nhi\u00ean n n\u00e0o th\u00ec b\u00e0i to\u00e1n c\u00f3 l\u1eddi gi\u1ea3i. B\u00e0i 26:M\u1ed9t \u00f4ng ch\u1ee7 x\u01b0\u1edfng \u0111\u00fac ti\u1ec1n c\u00f3 100 c\u00f4ng nh\u00e2n. M\u1ed7i s\u00e1ng \u00f4ng ta \u0111\u01b0a ra 1 kg","v\u00e0ng \u0111\u1ec3 \u0111\u00fac l\u1ea5y 100 \u0111\u1ed3ng ti\u1ec1n v\u00e0ng, m\u1ed7i \u0111\u1ed3ng ti\u1ec1n n\u1eb3ng 10g. Sau khi quan s\u00e1t m\u1ed9t v\u00e0i ng\u00e0y \u00f4ng nh\u1eadn th\u1ea5y c\u00f3 c\u00f4ng nh\u00e2n n\u00e0o \u0111\u00f3 \u0111\u00e3 \u0111\u00fac \u0111\u1ed3ng ti\u1ec1n ch\u1ec9 c\u00f3 9g. s\u1ed1 v\u00e0ng d\u01b0 ra anh ta gi\u1ea5u \u0111i. Sau khi suy t\u00ednh, \u00f4ng ta \u0111\u00e3 t\u00ecm ra \u0111\u01b0\u1ee3c ph\u01b0\u01a1ng ph\u00e1p ch\u1ec9 sau 1 l\u1ea7n c\u00e2n l\u00e0 x\u00e1c \u0111\u1ecbnh \u0111\u00fang k\u1ebb l\u1ea5y v\u00e0ng. \u00d4ng ta \u0111\u00e3 d\u00f9ng ph\u01b0\u01a1ng ph\u00e1p n\u00e0o? B\u00e0i 27: Hai du kh\u00e1ch \u0111i ra hoang m\u1ea1c. M\u1ed9t ng\u01b0\u1eddi mang theo 3 \u1ed5 b\u00e1nh m\u00ec, ng\u01b0\u1eddi kia mang 2 \u1ed5. H\u1ecd g\u1eb7p ng\u01b0\u1eddi th\u1ee9 3 c\u0169ng \u0111i t\u1edbi \u0111\u00f3, anh n\u00e0y \u0111ang \u0111\u00f3i m\u00e0 l\u1ea1i kh\u00f4ng mang b\u00e1nh m\u00ec n\u00ean ng\u1ecf \u00fd v\u1edbi 2 ng\u01b0\u1eddi ki cho \u0103n chung. Hai ng\u01b0\u1eddi kia \u0111\u1ed3ng \u00fd v\u00e0 trong b\u1eefa \u0103n c\u1ea3 ba ng\u01b0\u1eddi \u0111\u00e3 \u0103n l\u01b0\u1ee3ng b\u00e1nh m\u00ec nh\u01b0 nhau. \u0110\u1ec3 c\u00e1m \u01a1n, anh ch\u00e0ng \u0111\u00f3i b\u1ee5ng \u0111\u01b0a l\u1ea1i cho hai ng\u01b0\u1eddi b\u1ea1n \u0111\u1ed3ng h\u00e0nh 5 \u0111\u1ed3ng ti\u1ec1n v\u00e0ng (5 \u0111\u1ed3ng ti\u1ec1n v\u00e0ng m\u1ed7i \u0111\u1ed3ng b\u1eb1ng 20 xu) v\u00e0 \u0111\u1ec1 ngh\u1ecb h\u1ecd chia s\u1ed1 ti\u1ec1n \u0111\u00f3 v\u1edbi nhau t\u00f9y theo ai \u0111\u00e3 cho anh ta \u0103n bao nhi\u00eau. Ng\u01b0\u1eddi c\u00f3 2 \u1ed5 b\u00e1nh m\u00ec mu\u1ed1n l\u1ea5y 2 \u0111\u1ed3ng v\u00e0ng, nh\u01b0ng anh ch\u00e0ng c\u00f3 3 \u1ed5 b\u00e1nh m\u00ec l\u1ea1i n\u00f3i:\\\" Kh\u00f4ng \u0111\u01b0\u1ee3c, t\u00f4i ph\u1ea3i l\u1ea5y 4 \u0111\u1ed3ng c\u00f2n anh ch\u1ec9 \u0111\u01b0\u1ee3c 1 \u0111\u1ed3ng\\\". Th\u1ebf l\u00e0 cu\u1ed9c tranh c\u00e3i n\u1ed5 ra. M\u1ed9t v\u1ecb quan t a anh minh \u0111\u00e3 gi\u1ea3i quy\u1ebft xong v\u1ee5 ki\u1ec7n n\u00e0y, sau khi \u0111\u00e3 th\u1ef1c hi\u1ec7n \u0111\u00fang y\u00eau c\u1ea7u c\u1ee7a anh ch\u00e0ng th\u1ee9 3. H\u1ecfi v\u1ecb quan t\u00f2a \u1ea5y \u0111\u00e3 gi\u1ea3i quy\u1ebft nh\u01b0 th\u1ebf n\u00e0o? B\u00e0i 28: Hai ng\u01b0\u1eddi \u0111i du l\u1ecbch, trong b\u1eefa \u0103n m\u1ed9t ng\u01b0\u1eddi c\u1eaft 4 l\u00e1t b\u00e1nh m\u00ec, ng\u01b0\u1eddi kia c\u1eaft ba l\u00e1t. M\u1ed9t ng\u01b0\u1eddi \u0111\u1ed3ng h\u00e0nh \u0111i t\u1edbi v\u00e0 h\u1ecd m\u1eddi anh ta c\u00f9ng \u0103n. M\u1ed7i l\u00e1t b\u00e1nh m\u00ec \u0111\u01b0\u1ee3c chia l\u00e0m 3 ph\u1ea7n v\u00e0 m\u1ed7i ng\u01b0\u1eddi \u0103n 7 mi\u1ebfng nh\u01b0 th\u1ebf. Ng\u01b0\u1eddi th\u1ee9 3 g\u1eedi l\u1ea1i 7 \u0111\u1ed3ng ti\u1ec1n v\u00e0ng tr\u1ea3 cho hai ng\u01b0\u1eddi b\u1ea1n \u0111\u1ed3ng h\u00e0nh v\u1ec1 ph\u1ea7n b\u00e1nh m\u00ec m\u00ecnh \u0111\u00e3 \u0103n. H\u1ecfi hai ng\u01b0\u1eddi du l\u1ecbch kia m\u1ed7i ng\u01b0\u1eddi \u0111\u01b0\u1ee3c l\u1ea5y bao nhi\u00eau \u0111\u1ed3ng v\u1ec1 s\u1ed1 b\u00e1nh m\u00ec m\u00ecnh b\u1ecf ra? B\u00e0i 29: M\u1ed9t ng\u01b0\u1eddi n\u00f4ng d\u00e2n c\u00f3 12 \u0111\u1ed3ng c\u1ecf, ng\u01b0\u1eddi n\u00f4ng d\u00e2n th\u1ee9 2 c\u00f3 8 \u0111\u1ed3ng c\u1ecf, c\u00f2n ng\u01b0\u1eddi th\u1ee9 ba ch\u1eb3ng c\u00f3 \u0111\u1ed3ng c\u1ecf n\u00e0o. S\u1ed1 c\u1ecf m\u00e0 ba ng\u01b0\u1eddi n\u00e0y c\u1eaft tr\u00ean c\u00e1nh \u0111\u1ed3ng \u0111\u01b0\u1ee3c chia \u0111\u1ec1u. V\u00ec s\u1ed1 c\u1ecf nh\u1eadn \u0111\u01b0\u1ee3c, ng\u01b0\u1eddi th\u1ee9 3 mang \u0111\u1ebfn 20kg ti\u1ec3u m\u1ea1ch tr\u1ea3 cho 2 ng\u01b0\u1eddi t\u00f9y theo s\u1ed1 c\u1ecf m\u00e0 m\u1ed7i ng\u01b0\u1eddi \u0111\u00e3 cho anh ta. H\u1ecfi m\u1ed7i ch\u1ee7 \u0111\u1ed3ng c\u1ecf nh\u1eadn \u0111\u01b0\u1ee3c bao nhi\u00eau kg ti\u1ec3u m\u1ea1ch. B\u00e0i 30: M\u1ed9t b\u00e1c s\u0129 c\u00f3 20 ng\u01b0\u1eddi quen (11 \u0111\u00e0n \u00f4ng v\u00e0 9 ng\u01b0\u1eddi \u0111\u00e0n b\u00e0) v\u00e0 th\u01b0\u1eddng m\u1eddi h\u1ecd \u0111\u1ebfn nh\u00e0 m\u00ecnh ch\u01a1i. Trong m\u1ed7i d\u1ecbp \u0111\u1ec1 m\u1eddi 3 ng\u01b0\u1eddi \u0111\u00e0n \u00f4ng v\u00e0 2 ng\u01b0\u1eddi \u0111\u00e0n b\u00e0. H\u1ecfi b\u00e1c s\u0129 c\u1ea7n \u00edt nh\u1ea5t bao nhi\u00eau l\u1ea7n m\u1eddi \u0111\u1ec3 m\u1ecdi ng\u01b0\u1eddi kh\u00e1ch \u0111\u1ec1u c\u00f3 d\u1ecbp g\u1eb7p g\u1ee1, quen v\u1edbi nhau t\u1ea1i nh\u00e0 m\u00ecnh? B\u00e0i 31: Ba \u0111\u00f4i v\u1ee3 ch\u1ed3ng m\u1edbi c\u01b0\u1edbi -An,B\u00ecnh,C\u1ea3nh- \u0111i ch\u1ee3 hoa xu\u00e2n. C\u00e1c c\u00f4 v\u1ee3 t\u00ean Lan, My, Nh\u01b0. V\u00e0o ch\u1ee3, h\u1ecd chia tay, m\u1ed7i ng\u01b0\u1eddi m\u1ed7i ng\u00e3 t\u00ecm mua lo\u1ea1i hoa m\u00ecnh th\u00edch nh\u1ea5t. S\u1edf th\u00edch m\u1ed7i ng\u01b0\u1eddi m\u1ed7i kh\u00e1c v\u00e0 h\u1ecd mua 6 lo\u1ea1i hoa kh\u00e1c nhau, v\u1edbi gi\u00e1 ti\u1ec1n kh\u00e1c nhau. V\u1ec1 nh\u00e0 h\u1ecd ph\u00e1t hi\u1ec7n ra r\u1eb1ng s\u1ed1 b\u00f4ng hoa m\u1ed7i ng\u01b0\u1eddi mua b\u1eb1ng \u0111\u00fang gi\u00e1 mua 1 b\u00f4ng hoa, t\u00ednh ra \u0111\u1ed3ng.Ngo\u00e0i ra An mua nhi\u1ec1u h\u01a1n My 9 b\u00f4ng, B\u00ecnh nhi\u1ec1u h\u01a1n Lan 7 b\u00f4ng v\u00e0 m\u1ed7i anh ch\u1ed3ng mua nhi\u1ec1u h\u01a1n v\u1ee3 m\u00ecnh \u0111\u00fang 48 \u0111\u1ed3ng. B\u1ea1n h\u00e3y cho bi\u1ebft c\u00f4 n\u00e0o l\u00e0 v\u1ee3 c\u1ee7a anh n\u00e0o.","B\u00e0i 32: B\u00e0 \u1edf qu\u00ea l\u00ean cho ba anh em An, B\u00ecnh, Chi 24 qu\u1ea3 t\u00e1o. S\u1ed1 t\u00e1o m\u1ed7i em nh\u1eadn \u0111\u01b0\u1ee3c b\u1eb1ng \u0111\u00fang s\u1ed1 tu\u1ed5i c\u1ee7a m\u00ecnh tr\u1eeb \u0111i 3. Chi r\u1ea5t th\u00f4ng minh \u0111\u1ec1 ngh\u1ecb nh\u01b0 sau: -Em chia s\u1ed1 t\u00e1o c\u1ee7a em ra l\u00e0m \u0111\u00f4i, em gi\u1eef 1 ph\u1ea7n c\u00f2n ph\u1ea7n kia chia \u0111\u00f4i cho 2 anh. Sau \u0111\u00f3 \u0111\u1ebfn l\u01b0\u1ee3t anh B\u00ecnh chia \u0111\u00f4i s\u1ed1 t\u00e1o c\u1ee7a m\u00ecnh, gi\u1eef l\u1ea1i 1 ph\u1ea7n c\u00f2n ph\u1ea7n c\u00f2n l\u1ea1i chia \u0111\u00f4i cho anh An v\u00e0 em. Sau c\u00f9ng \u0111\u1ebfn l\u01b0\u1ee3t anh An c\u0169ng l\u00e0m nh\u01b0 th\u1ebf. V\u1eady l\u00e0 ba ch\u00fang ta s\u1ebd c\u00f3 s\u1ed1 t\u00e1o nh\u01b0 nhau. B\u1ea1n h\u00e3y cho bi\u1ebft s\u1ed1 tu\u1ed5i c\u1ee7a 3 em \u0111\u00f3. B\u00e0i 33: Tr\u00ean b\u00e0n \u0111\u1ec3 m\u1ed9t \u0111\u0129a k\u1eb9o. M\u1ed9t em b\u00e9 \u0111i qua l\u1ea5y m\u1ed9t n\u1eefa s\u1ed1 k\u1eb9o v\u00e0 th\u00eam 1 chi\u1ebfc. Em th\u1ee9 2 l\u1ea5y m\u1ed9t n\u1eefa s\u1ed1 k\u1eb9o c\u00f2n l\u1ea1i v\u00e0 th\u00eam 1 chi\u1ebfc. Em th\u1ee9 3 l\u1ea5y m\u1ed9t n\u1eefa s\u1ed1 k\u1eb9o c\u00f2n l\u1ea1i v\u00e0, ngh\u0129 th\u1ebf n\u00e0o, b\u1ecf tr\u1edf l\u1ea1i m\u1ed9t chi\u1ebfc v\u00e0o \u0111\u0129a. Cu\u1ed1i c\u00f9ng tr\u00ean \u0111\u0129a c n l\u1ea1i 4 chi\u1ebfc. H\u1ecfi l\u00fac \u0111\u1ea7u \u0111\u0129a c\u00f3 m\u1ea5y chi\u1ebfc k\u1eb9o? B\u00e0i 34: Tr\u00ean b\u00e0n c\u1edd vua l\u1ea5y 50 \u00f4 t\u00f9y \u00fd v\u00e0 \u0111\u00e1nh s\u1ed1 t\u1eeb 1 \u0111\u1ebfn 50. L\u1ea5y 50 qu\u00e2n c\u1edd c\u0169ng \u0111\u00e1nh s\u1ed1 t\u1eeb 1 \u0111\u1ebfn 50 v\u00e0 \u0111\u1eb7t t\u00f9y \u00fd m\u1ed7i qu\u00e2n c\u1edd v\u00e0o 1 \u00f4 c\u1ee7a b\u00e0n c\u1edd. Ta g\u1ecdi 1 l\u1ea7n chuy\u1ec3n l\u00e0 vi\u1ec7c \u0111\u01b0a 1 qu\u00e2n c\u1edd t\u1eeb 1 \u00f4 \u0111\u1ebfn 1 \u00f4 tr\u1ed1ng n\u00e0o \u0111\u00f3. H\u00e3y ch\u1ee9ng t\u1ecf r\u1eb1ng nhi\u1ec1u nh\u1ea5t ch\u1ec9 c\u1ea7n 75 l\u1ea7n chuy\u1ec3n s\u1ebd \u0111\u01b0a \u0111\u01b0\u1ee3c 50 qu\u00e2n c\u1edd v\u1ec1 c\u00e1c \u00f4 s\u1ed1 t\u01b0\u01a1ng \u1ee9ng. B\u00e0i 35: Trong m\u1ed9t cu\u1ed9c thi \u0111\u1ea5u v\u1eadt, \u0111o\u1ea1t gi\u1ea3i \u0111\u1ea7u l\u00e0 c\u00e1c v\u1eadn \u0111\u1ed9ng vi\u00ean mang s\u1ed1 \u00e1o t\u1eeb 1,2,3 v\u00e0 4 , nh\u01b0ng kh\u00f4ng ai c\u00f3 s\u1ed1 \u00e1o tr\u00f9ng v\u1edbi th\u1ee9 t\u1ef1 gi\u1ea3i.H\u00e3y x\u00e1c \u0111\u1ecbnh th\u1ee9 t\u1ef1 c\u1ee7a gi\u1ea3i bi\u1ebft r\u1eb1ng: V\u1eadn \u0111\u1ed9ng vi\u00ean \u0111o\u1ea1t gi\u1ea3i 4 c\u00f3 s\u1ed1 \u00e1o tr\u00f9ng v\u1edbi th\u1ee9 t\u1ef1 gi\u1ea3i c\u1ee7a v\u1eadn \u0111\u1ed9ng vi\u00ean c\u00f3 s\u1ed1 \u00e1o nh\u01b0 th\u1ee9 t\u1ef1 gi\u1ea3i c\u1ee7a v\u1eadn \u0111\u1ed9ng vi\u00ean mang \u00e1o s\u1ed1 2. V\u1eadn \u0111\u1ed9ng vi\u00ean mang \u00e1o s\u1ed1 3 kh\u00f4ng \u0111o\u1ea1t gi\u1ea3i nh\u1ea5t. B\u00e0i 36: M\u1ed9t anh b\u1ea1n tr\u1ebb h\u1ecfi s\u1ed1 \u0111i\u1ec7n tho\u1ea1i c\u1ee7a 1 b\u1ea1n g\u00e1i m\u1edbi quen. C\u00f4 ta tr\u1ea3 l\u1eddi nh\u01b0 sau:T\u00f4i c\u00f3 t\u1edbi 4 s\u1ed1 \u0111i\u1ec7n tho\u1ea1i l\u1eadn, trong \u0111\u00f3 m\u1ed7i s\u1ed1 kh\u00f4ng c\u00f3 ch\u1eef s\u1ed1 n\u00e0o c\u00f3 m\u1eb7t 2 l\u1ea7n. C\u00e1c s\u1ed1 \u0111\u00f3 c\u00f3 t\u00ednh ch\u1ea5t chung l\u00e0 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a m\u1ed7i s\u1ed1 \u0111\u1ec1 b\u1eb1ng 10. N\u1ebfu l\u1ea5y m\u1ed7i s\u1ed1 c\u1ed9ng v\u1edbi s\u1ed1 vi\u1ebft theo th\u1ee9 t\u1ef1 ng\u01b0\u1ee3c c\u1ee7a n\u00f3 th\u00ec \u0111\u01b0\u1ee3c 4 s\u1ed1 b\u1eb1ng nhau v\u00e0 l\u00e0 s\u1ed1 c\u00f3 5 ch\u1eefng s\u1ed1 gi\u1ed1ng nhau. \u0110\u1ed1i v\u1edbi nh\u01b0 v\u1eady l\u00e0 \u0111\u1ee7 r\u1ed3i ph\u1ea3i kh\u00f4ng \u1ea1 ? B\u1ea1n h\u00e3y gi\u00fap anh b\u1ea1n tr\u1ebb \u0111\u00f3 bi\u1ebft r\u1eb1ng s\u1ed1 \u0111i\u1ec7n tho\u1ea1i trong th\u00e0nh ph\u1ed1 trong kho\u1ea3ng t\u1eeb 20000 \u0111\u1ebfn 99999 B\u00e0i 37: Trong gi\u1edd ngh\u1ec9 \u1edf m\u1ed9t h\u1ed9i ngh\u1ecb, c\u00e1c \u0111\u1ed3ng nghi\u1ec7p h\u1ecfi m\u1ed9t gi\u00e1o s\u01b0 xem \u00f4ng ta c\u00f3 m\u1ea5y con v\u00e0 ch\u00fang bao nhi\u00eau tu\u1ed5i. Gi\u00e1o s\u01b0 tr\u1ea3 l\u1eddi: -T\u00f4i c\u00f3 3 con trai. C\u00f3 s\u1ef1 tr\u00f9ng h\u1ee3p l\u00fd th\u00fa l\u00e0 ng\u00e0y sinh c\u1ee7a ch\u00fang \u0111\u1ec1u l\u00e0 ng\u00e0y h\u00f4m nay, tu\u1ed5i ch\u00fang c\u1ed9ng l\u1ea1i b\u1eb1ng ng\u00e0y h\u00f4m nay v\u00e0 \u0111em nh\u00e2n v\u1edbi nhau th\u00ec t\u00edch l\u00e0 36. M\u1ed9t \u0111\u1ed3ng nghi\u1ec7p n\u00f3i: -Ch\u1ec9 nh\u01b0 v\u1eady th\u00ec ch\u01b0a x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c tu\u1ed5i c\u1ee7a b\u1ecdn tr\u1ebb. -\u1ed2, \u0111\u00fang v\u00e2y. T\u00f4i qu\u00ean kh\u00f4ng n\u00f3i th\u00eam r\u1eb1ng: Khi ch\u00fang t\u00f4i ch\u1edd sinh \u0111\u1ee9a th\u1ee9 3 th\u00ec 2 \u0111\u1ee9a l\u1edbn \u0111\u00e3 \u0111\u01b0\u1ee3c g\u1eedi v\u1ec1 qu\u00ea v\u1edbi \u00f4ng b\u00e0. -Xin c\u00e1m \u01a1n ng\u00e0i, gi\u1edd th\u00ec t\u00f4i \u0111\u00e3 bi\u1ebft tu\u1ed5i c\u1ee7a b\u1ecdn tr\u1ebb r\u1ed3i. V\u1eady tu\u1ed5i c\u1ee7a m\u1ed7i c\u1eadu con trai l\u00e0 bao nhi\u00eau v\u00e0 ng\u00e0y h\u00f4m \u0111\u00f3 l\u00e0 ng\u00e0y n\u00e0o trong th\u00e1ng? B\u00e0i 38: M\u1ed9t c\u00e2y b\u00e8o tr\u00f4i theo d ng n\u01b0\u1edbc v\u00e0 m\u1ed9t ng\u01b0\u1eddi b\u01a1i ng\u01b0\u1ee3c d ng n\u01b0\u1edbc c\u00f9ng xu\u1ea5t ph\u00e1t v\u00e0o 1 th\u1eddi \u0111i\u1ec3m t\u1ea1i m\u1ed9t c\u1ed9t m\u1ed1c. Ng\u01b0\u1eddi b\u01a1i ng\u01b0\u1ee3c d ng n\u01b0\u1edbc \u0111\u01b0\u1ee3c 20 ph\u00fat th\u00ec","quay l\u1ea1i b\u01a1i xu\u00f4i d ng v\u00e0 g\u1eb7p c\u00e2y b\u00e8o c\u00e1ch c\u1ed9t m\u1ed1c 4 km. H\u00e3y t\u00ednh v\u1eadn t\u1ed1c c\u1ee7a d\u00f2ng n\u01b0\u1edbc bi\u1ebft r\u1eb1ng v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi b\u01a1i l\u00e0 kh\u00f4ng \u0111\u1ed5i. B\u00e0i 39: C\u00f3 7 ng\u01b0\u1eddi s\u1ed1ng chung trong 1 c\u0103n nh\u00e0 nh\u1ecf. H\u1ecd \u0111\u00e3 cho nhau vay nh\u1eefng m\u00f3n ti\u1ec1n nh\u1ecf. M\u1ed7i ng\u01b0\u1eddi \u0111\u1ec1u ghi s\u1ed1 ti\u1ec1n m\u00ecnh vay v\u00e0 s\u1ed1 ti\u1ec1n m\u00ecnh cho vay nh\u01b0ng kh\u00f4ng ghi cho ai vay v\u00e0 vay c\u1ee7a ai. Tr\u01b0\u1edbc khi chia tay , h\u1ecd quy\u1ebft \u0111\u1ecbnh thanh to\u00e1n n\u1ee3 n\u1ea7n v\u1edbi nhau v\u00e0 \u0111\u00e3 thanh to\u00e1n r\u1ea5t s\u00f2ng ph\u1eb3ng b\u1eb1ng 1 c\u00e1ch r\u1ea5t \u0111\u01a1n gi\u1ea3n. \u0110\u00f3 l\u00e0 c\u00e1ch n\u00e0o v\u1eady? B\u00e0i 40: Tr\u00ean m\u1ed9t b\u00e0n c\u1edd 8*8 \u00f4. Qu\u00e2n m\u00e3 trong c\u1edd vua t\u1eeb \u00f4 g\u00f3c d\u01b0\u1edbi b\u00ean tr\u00e1i t\u1edbi \u00f4 g\u00f3c tr\u00ean b\u00ean ph\u1ea3i sao cho m\u1ed7i \u00f4 c\u1ee7a b\u00e0n c\u1edd m\u00e3 \u0111i qua d\u00fang 1 l\u1ea7n \u0111\u01b0\u1ee3c hay kh\u00f4ng? (qu\u00e2n m\u00e3 \u0111i theo \u0111\u00fang quy t\u1eafc tr\u00ean b\u00e0n c\u1edd vua). 25.To\u00e1n KH\u00d3 B\u00e0i 1: T\u1ed5ng c\u1ee7a c\u00e1c t\u00edch 2 s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean ti\u1ebfp T\u00ednh t\u00edch S = 1x2 + 2x3 + 3x4 + \u2026\u2026\u2026\u2026\u2026\u2026 + 11x12 + 12x13 Gi\u1ea3i C\u00e1ch 1: S = 1x2 + 2x3 + 3x4 + \u2026\u2026\u2026\u2026\u2026\u2026 + 11x12 + 12x13 3S=1x2x3 + 2x3x3 + 3x4x3+ \u2026\u2026\u2026. + 11x12x3 + 12x13x3 Ta l\u1ea5y K = 1x2x3 +2x3x4 + 3x4x5 + \u2026\u2026 + 11x12x13 + 12x13x14 - 3S = 1x2x3 + 2x3x3 + 3x4x3+ \u2026\u2026\u2026 + 11x12x3 + 12x13x3 ------------------------------------------------------------------------------------ K \u2013 3S = 0 + 2x3x1 + 3x4x2 + \u2026\u2026 .. + 11x12x10 + 12x13x11 K \u2013 3S = K \u2013 12x13x14 T\u1eeb \u0111\u00f3 suy ra: 3S = 12x13x14 S = 4x13x14 = 728 C\u00e1ch 2: S x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + \u2026. + 11x12x(13-10) + 12x13x(14-11) S x 3 = 1x2x3 + 2x3x4 \u2013 2x3x1 + 3x4x5 \u2013 3x4x2 + \u2026..+ 11x12x13 \u2013 11x12x10 +12x13x14 \u2013 12x13x11 S x 3 = 12 x 13 x14","S = 4 x 13 x 14 S = 728 B\u00e0i 2: T\u1ed5ng c\u00e1c ph\u00e2n s\u1ed1 Cho A= 1\/2 + 1\/4 + 1\/8 + 1\/16 + 1\/32 + 1\/64 Gi\u1ea3i C\u00e1ch 1: C\u00e1ch 2: B\u00e0i 3: T\u1ed5ng c\u00e1c ph\u00e2n s\u1ed1 Cho A= 1\/2 + 1\/6 + 1\/12 + 1\/20 + 1\/30 + 1\/42 Gi\u1ea3i","B\u00e0i 4: T\u1ed5ng c\u00e1c ph\u00e2n s\u1ed1 Cho A= 1\/2 + 1\/6 + 1\/12 + 1\/20 + 1\/30 + ... + 1\/n . Bi\u1ebft A= 49\/50 . T\u00ecm n. Gi\u1ea3i B\u00e0i 5:","B\u00e0i 6: T\u00ednh A = 2008+2007\/2+2006\/3+2005\/4+...+2\/2007+1\/2008 1\/2 + 1\/3 + 1\/4 +\u2026\u2026\u2026\u2026..+ 1\/2008 + 1\/2009 Ta c\u00f3 t\u1eed s\u1ed1 b\u1eb1ng: 2008+2007\/2+2006\/3+2005\/4+\u2026..+2\/2007+1\/2008 (Ph\u00e2n t\u00edch 2008 th\u00e0nh 2008 con s\u1ed1 1 r\u1ed3i \u0111\u01b0a v\u00e0o c\u00e1c nh\u00f3m) = (1 + 2007\/2) + (1 + 2006\/3) + (1 + 2005\/4) +... + (1 + 2\/2007) + ( 1 + 1\/2008) + (1) = 2009\/2 + 2009\/3 + 2009\/\/4 + \u2026\u2026. + 2009\/2007 + 2009\/2008 + 2009\/2009 = 2009 x (1\/2 + 1\/3 + 1\/4 + ... + 1\/2007 + 1\/2008 + 1\/2009) M u s\u1ed1: 1\/2 + 1\/3 + 1\/4 + ... + 1\/2007 + 1\/2008 + 1\/2009 V\u1eady A = 2009 B\u00e0i 7","B\u00e0i 8: B\u00e0i 9: Cho A = 1\/2 + 1\/3 + 1\/4 + 1\/5 +1\/6 +.................+ 1\/16 + 1\/17 Ch\u1ee9ng minh r\u1eb1ng A kh\u00f4ng ph\u1ea3i l\u00e0 s\u1ed1 t\u1ef1 nhi\u00ean. Gi\u1ea3i Ta c\u00f3: A = (1\/2 + 1\/3 + 1\/4 + 1\/5) + (1\/6 + 1\/7 + 1\/8) + (1\/9 + 1\/10 + 1\/11) + (1\/12 + 1\/13 + 1\/14) + (1\/15 + 1\/16 + 1\/17) < (1\/2 + 1\/3 + 1\/4 + 1\/5) + 3(1\/6) + 3(1\/9) + 3(1\/12) + 3(1\/15) =","2(1\/2 + 1\/3 + 1\/4 + 1\/5) < 2(1\/2 + 1\/2 + 1\/4 + 1\/4) = 3 M\u1eb7t kh\u00e1c A = (1\/2 + 1\/3 + 1\/4) + (1\/5 + 1\/6 + 1\/7 + 1\/8) + (1\/9 + 1\/10 + 1\/11 + 1\/12) + (1\/13 + 1\/14 + 1\/15 + 1\/16) + 1\/17 > (1\/2 + 1\/3 + 1\/4) + 4(1\/8) + 4(1\/12) + 4(1\/16) = 2(1\/2 + 1\/3 + 1\/4) > 2(1\/2 + 1\/4 + 1\/4) = 2 => 2 < A < 3 V\u1ead A h\u00f4ng l\u00e0 s\u1ed1 t\u1ef1 nhi\u00ean B\u00e0i 10: T\u00ednh: A=1x2x3+2x3x4+\u2026+100x101x102 A = 1x2x3 + 2x3x4 +\u2026+ 100x101x102 Nh\u00e2n A v\u1edbi 4 ta c\u00f3 : A x 4 = 1x2x3x4 + 2x3x4x 4 + 3x4x5x4 +\u2026+100x101x102x4 A x 4 = 1x2x3x4 + 2x3x4x(5-1) + 3x4x5x(6-2) + ... + 100x101x102x(103 - 99) A x 4 = 1x2x3x4 + 2x3x4x5 - 1x2x3x4 + 3x4x5x6 - 2x3x4x5 + ... + 100x101x102x103 - 99x100x1001x102 Sau khi c\u1ed9ng - tr\u1eeb gi\u1ea3n \u01b0\u1edbc ta c\u00f3 : A x 4 = 100x101x102x103 A = 100 x101x102x103 : 4 = 26527650 B\u00e0i 11: Cho m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 2014 ch\u1eef s\u1ed1. Bi\u1ebft r\u1eb1ng v\u1edbi hai ch\u1eef s\u1ed1 li\u00ean ti\u1ebfp theo th\u1ee9 t\u1ef1 \u0111\u00e3 vi\u1ebft th\u00ec t\u1ea1o th\u00e0nh s\u1ed1 c\u00f3 hai ch\u1eef s\u1ed1 chia h\u1ebft cho 17 ho\u1eb7c chia h\u1ebft cho 23. N\u1ebfu ch\u1eef s\u1ed1 cu\u1ed1i c\u00f9ng c\u1ee7a s\u1ed1 \u0111\u00f3 l\u00e0 ch\u1eef s\u1ed1 1 th\u00ec ch\u1eef s\u1ed1 \u0111\u1ea7u ti\u00ean l\u00e0 ch\u1eef s\u1ed1 n\u00e0o? Ta suy lu\u1eadn d\u1ea7n th\u1ebf n\u00e0y: Ch\u1eef s\u1ed1 cu\u1ed1i c\u00f9ng l\u00e0 1 th\u00ec ch\u1eef s\u1ed1 li\u1ec1n tr\u01b0\u1edbc ph\u1ea3i l\u00e0 5 \u0111\u1ec3 51 chia h\u1ebft cho 17 (51:17=3) \u2026\u2026\u202651 Tr\u01b0\u1edbc ch\u1eef s\u1ed1 5 ph\u1ea3i l\u00e0 8 \u0111\u1ec3 c\u00f3 85:17=5 \u2026\u2026\u2026.851 Tr\u01b0\u1edbc ch\u1eef s\u1ed1 8 ph\u1ea3i l\u00e0 6 \u0111\u1ec3 c\u00f3 68:17=4 \u2026\u2026\u2026.6851 Tr\u01b0\u1edbc ch\u1eef s\u1ed1 6 ph\u1ea3i l\u00e0 4 \u0111\u1ec3 c\u00f3 46:23=2 \u2026\u2026\u2026.46851 Tr\u01b0\u1edbc ch\u1eef s\u1ed1 4 ph\u1ea3i l\u00e0 3 \u0111\u1ec3 c\u00f3 34:17=2 \u2026\u2026\u2026.346851 Tr\u01b0\u1edbc ch\u1eef s\u1ed1 3 ph\u1ea3i l\u00e0 2 \u0111\u1ec3 c\u00f3 23:23=1 \u2026\u2026\u2026.2346851 Tr\u01b0\u1edbc ch\u1eef s\u1ed1 2 ph\u1ea3i l\u00e0 9 \u0111\u1ec3 c\u00f3 92:23=4 \u2026\u2026\u2026.92346851 Tr\u01b0\u1edbc ch\u1eef s\u1ed1 9 ph\u1ea3i l\u00e0 6 \u0111\u1ec3 c\u00f3 69:23=3 \u2026\u2026\u2026.692346851 \u2026\u2026\u2026\u2026.. Ti\u1ebfp t\u1ee5c: \u2026\u2026\u2026\u2026.92346 92346 92346 851 Ta th\u1ea5y quy lu\u1eadt l\u1eadp nhi\u1ec1u l\u1ea7n l\u1ea1i 5 ch\u1eef s\u1ed1: 9;2;3;4;6 cu\u1ed1i c\u00f9ng l\u00e0 851.","B\u1ecf 3 ch\u1eef s\u1ed1 cu\u1ed1i c\u00f9ng (851) th\u00ec c\u00f2n l\u1ea1i: 2014-3=2011 (ch\u1eef s\u1ed1) Chia nh\u00f3m 5 th\u00ec \u0111\u01b0\u1ee3c: 2011 : 5 = 402 (nh\u00f3m 5) d\u01b0 1. Ch\u1eef s\u1ed1 cu\u1ed1i c\u00f9ng trong nh\u00f3m 5 l\u00e0 ch\u1eef s\u1ed1 6. V\u1eady ch\u1eef s\u1ed1 \u0111\u1ea7u ti\u00ean trong d\u1ea1y l\u00e0 6 (6 92346 92346 92346 \u2026\u2026\u2026\u2026. 92346 92346 851) B\u00e0i 12: T\u00ednh t\u1ed5ng : A=38\/25 + 9\/10 - 11\/15 + 13\/21 - 15\/28 + 17\/36 - ................+197\/4851- 199\/4950 T\u1eeb: 9\/10 - 11\/15 + 13\/21 - 15\/28 + 17\/36 \u2013 19\/45... + 197\/4851 - 199\/4950 Ta c\u00f3 th\u1ec3 vi\u1ebft l\u1ea1i: (9\/10 - 11\/15) + (13\/21 - 15\/28) + 17\/36 \u2013 19\/45... + (197\/4851 - 199\/4950) Ta th\u1ea5y : (9\/10 - 11\/15) = 1\/6 = 1\/(2x3) = 1\/2 \u2013 1\/3 (13\/21 \u2013 15\/28) = 1\/12 = 1\/(3x4) = 1\/3 \u2013 1\/4 (17\/36 \u2013 19\/45) = 1\/20 = 1\/(4x5) = 1\/4 \u2013 1\/5 \u2026\u2026\u2026\u2026\u2026\u2026.. (197\/4851 \u2013 199\/4950) = 1\/2450 = 1\/(49x50) = 1\/49 \u2013 1\/50 Ta \u0111\u01b0\u1ee3c: 9\/10 - 11\/15 + 13\/21 - 15\/28 + 17\/36 \u2013 19\/45... + 197\/4851 - 199\/4950 = 1\/2-1\/3+1\/3-1\/4+1\/4-1\/5+ \u2026. + 1\/49-1\/50 = 1\/2 \u2013 1\/50 = 24\/50 V\u1eady : A = 38\/25 + 24\/50 = 2 A=2 B\u00e0i 13: Cho d\u00e3y s\u1ed1: 4\/3;9\/8;16\/15;25\/24;36\/35;....H\u00e3y t\u00ecm s\u1ed1 h\u1ea1ng th\u1ee9 98 v\u00e0 t\u00ednh t\u00edch c\u1ee7a 98 s\u1ed1 h\u1ea1ng \u0111\u1ea7u ti\u00ean c\u1ee7a d\u00e3y s\u1ed1. Gi\u1ea3i","B\u00e0i 14: Trong m\u1ed9t gi\u1ea3i b\u00f3ng \u0111\u00e1 c\u00f3 k \u0111\u1ed9i tham gia thi \u0111\u1ea5u v ng tr n 1 l\u01b0\u1ee3t (2 \u0111\u1ed9i b\u1ea5t k\u00ec thi \u0111\u1ea5u v\u1edbi nhau m\u1ed9t tr\u1eadn).\u0110\u1ed9i th\u1eafng \u0111\u01b0\u1ee3c 3 \u0111i\u1ec3m. \u0110\u1ed9i h a \u0111\u01b0\u1ee3c 1 \u0111i\u1ec3m v\u00e0 \u0111\u1ed9i thua kh\u00f4ng \u0111\u01b0\u1ee3c \u0111i\u1ec3m n\u00e0o. K\u1ebft th\u00fac gi\u1ea3i, ng\u01b0\u1eddi ta nh\u1eadn th\u1ea5y r\u1eb1ng s\u1ed1 tr\u1eadn th\u1eafng-thua g\u1ea5p \u0111\u00f4i s\u1ed1 tr\u1eadn h a v\u00e0 t\u1ed5ng s\u1ed1 \u0111i\u1ec3m c\u00e1c \u0111\u1ed9i l\u00e0 176. H\u00e3y t\u00ecm k ? Tr\u1eadn th\u1eafng 3 \u0111i\u1ec3m, tr\u1eadn h a 2 \u0111i\u1ec3m (v\u00ec m\u1ed7i \u0111\u1ed9i \u0111\u01b0\u1ee3c 1 \u0111i\u1ec3m). s\u1ed1 tr\u1eadn th\u1eafng-thua g\u1ea5p \u0111\u00f4i s\u1ed1 tr\u1eadn h a T\u1ed5ng s\u1ed1 \u0111i\u1ec3m l\u00e0 176 \u0111i\u1ec3m. T\u1ec9 s\u1ed1 \u0111i\u1ec3m cho tr\u1eadn th\u1eafng-thua v\u00e0 h\u00f2a l\u00e0: (3x2) \/ (2x1) = 3\/1 T\u1ed5ng s\u1ed1 ph\u1ea7n b\u1eb1ng nhau: 1 + 3 = 4 (ph\u1ea7n) S\u1ed1 \u0111i\u1ec3m cho c\u00e1c \u0111\u1ed9i h\u00f2a l\u00e0: 176 : 4 = 44 (\u0111i\u1ec3m) S\u1ed1 tr\u1eadn h\u00f2a l\u00e0: 44 : 2 = 22 (tr\u1eadn) S\u1ed1 \u0111i\u1ec3m cho c\u00e1c tr\u1eadn th\u1eafng thua l\u00e0 : 176 \u2013 44 = 132 (\u0111i\u1ec3m) S\u1ed1 tr\u1eadn th\u1eafng thua l\u00e0 : 132 : 3 = 44 (tr\u1eadn) T\u1ed5ng s\u1ed1 c\u00e1c tr\u1eadn \u0111\u1ea5u l\u00e0 : 22 + 44 = 66 (tr\u1eadn) Do k l\u00e0 s\u1ed1 \u0111\u1ed9i n\u00ean s\u1ed1 tr\u1eadn \u0111\u1ea5u s\u1ebd l\u00e0 : k x (k-1) : 2","Ta \u0111\u01b0\u1ee3c : k x (k-1) : 2 = 66 k x (k-1) = 66x2 = 132 Do k v\u00e0 (k-1) l\u00e0 2 s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean ti\u1ebfp v\u00e0 132 = 12 x 11 n\u00ean k = 12 (Hay c\u00f3 12 \u0111\u1ed9i thi \u0111\u1ea5u.) B\u00e0i 15: Tinh: A = 9+99+999+....+9.....9(co 50 chu so 9) Ta th\u1ea5y: 9 = 10 - 1 99 = 100 - 1 999 = 1000 - 1 .... 99...99 = 100...00 - 1 (50 ch\u1eef s\u1ed1 0) Suy ra: 9 + 99 + 999 + 9999 + 99........99 (50 ch\u1eef s\u1ed1 9) = (10 - 1) + (100 - 1) + ... + (100...00 - 1) = (10 + 100 + ... + 100...00) - (1 + 1 + 1 + ...+ 1) (50 ch\u1eef s\u1ed1 1 c\u1ed9ng v\u1edbi nhau) = 111....10 - 50 (50 ch\u1eef s\u1ed1 1) = 111....1160 (48 ch\u1eef s\u1ed1 1) B\u00e0i 16: Cho A = 671 x 999\u2026997 + 2013 (th\u1eeba s\u1ed1 999\u2026997 c\u00f3 t\u1ea5t c\u1ea3 99 ch\u1eef s\u1ed1 9) T\u00ednh t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a A. A = 671 x 99\u2026997 + 2015 ( th\u1eeba s\u1ed1 99\u2026997 c\u00f3 99 ch\u1eef s\u1ed1 9) = 671 x 100..00 \u2013 671 x 3 + 2015 ( s\u1ed1 100..00 c\u00f3 100 ch\u1eef s\u1ed1 0 ) = 67100\u202600 \u2013 2013 + 2015 = 67100\u202600 + 2 = 67100..02 V\u1eady t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a A l\u00e0: 6 + 7 + 1 + 2 = 16 \u0110\u00e1p s\u1ed1: 16 B\u00e0i 17:","Tinh: A = 9+99+999+....+9.....9 (co 50 chu so 9) Ta th\u1ea5y: 9 = 10 - 1 99 = 100 - 1 999 = 1000 - 1 .... 99...99 = 100...00 - 1 (50 ch\u1eef s\u1ed1 0) Suy ra: 9 + 99 + 999 + 9999 + 99........99 (50 ch\u1eef s\u1ed1 9) = (10 - 1) + (100 - 1) + ... + (100...00 - 1) = (10 + 100 + ... + 100...00) - (1 + 1 + 1 + ...+ 1) (50 ch\u1eef s\u1ed1 1 c\u1ed9ng v\u1edbi nhau) = 111....10 - 50 (50 ch\u1eef s\u1ed1 1) = 111....1060 (48 ch\u1eef s\u1ed1 1) B\u00e0i 17b: T\u00ednh: A=5+55+555+.......+55...55(co 50 chu so 5) A = 5\/9 x (9+99+999+\u2026+99\u202699) (c\u00f3 50 ch\u1eef s\u1ed1 9) =5\/9 x (10-1 + 100-1 + 1000-1 +\u2026+ 100..00-1) =5\/9 x (10+100+1000+\u2026+100..00 \u2013 50) =5\/9 x (111..110 \u2013 50) (111\u2026110 c\u00f3 50 ch\u1eef s\u1ed1 1) = 5\/9 x 111\u2026060 (c\u00f3 48 ch\u1eef s\u1ed1 5) = 555\u202655300\/9 (c\u00f3 48 ch\u1eef s\u1ed1 5) C\u00f4ng th\u1ee9c t\u1ed5ng qu\u00e1t: A = a+aa+aaa+\u2026+aa\u2026aa (c\u00f3 n ch\u1eef s\u1ed1 a) A=",""]