Nh\u1eadn bi\u1ebft c\u00e1c b\u1ed9 s\u1ed1 k\u00e9p trong l\u00f4 \u0111\u1ec1<\/strong> bao g\u1ed3m k\u00e9p b\u1eb1ng, k\u00e9p \u00e2m, k\u00e9p l\u1ec7ch v\u00e0 s\u00e1t k\u00e9p (\u00e1p k\u00e9p) l\u00e0 ki\u1ebfn th\u1ee9c r\u1ea5t quan tr\u1ecdng. \u0110\u00e2y l\u00e0 nh\u1eefng d\u1ea1ng l\u00f4 \u0111\u1ec1 kh\u00f4ng th\u1ec3 b\u1ecf qua \u0111\u1ed1i v\u1edbi b\u1ea5t k\u1ef3 ai mu\u1ed1n ki\u1ebfm ti\u1ec1n t\u1eeb k\u1ebft qu\u1ea3 x\u1ed5 s\u1ed1 ki\u1ebfn thi\u1ebft 3 mi\u1ec1n. <\/p>\n K\u00e9p b\u1eb1ng l\u00e0 t\u1eadp h\u1ee3p nh\u1eefng con s\u1ed1 tr\u00f9ng nhau c\u1ea3 h\u00e0ng ch\u1ee5c v\u00e0 h\u00e0ng \u0111\u01a1n v\u1ecb. C\u1ee5 th\u1ec3 l\u00e0 10 con s\u1ed1 sau \u0111\u00e2y: 00, 11, 22, 33, 44, 55, 66, 77, 88, 99<\/p>\n Do b\u1ed9 s\u1ed1 k\u00e9p l\u1ec7ch \u0111\u01b0\u1ee3c h\u00ecnh th\u00e0nh d\u1ef1a tr\u00ean \u201cb\u00f3ng s\u1ed1\u201d v\u00ec v\u1eady m\u00e0 tr\u01b0\u1edbc h\u1ebft c\u1ea7n xem l\u1ea1i ki\u1ebfn th\u1ee9c b\u00f3ng trong l\u00f4 \u0111\u1ec1. \u0110\u1ed1i v\u1edbi k\u00e9p l\u1ec7ch th\u00ec \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh t\u1eeb b\u00f3ng d\u01b0\u01a1ng. X\u00e1c \u0111\u1ecbnh nh\u1eefng b\u1ed9 s\u1ed1 b\u00f3ng b\u1eb1ng nh\u1eefng y\u1ebfu t\u1ed1 sau: nh\u1eefng s\u1ed1 c\u00f3 1 s\u1ed1 tr\u00f9ng nhau, s\u1ed1 c\u00f2n l\u1ea1i l\u00e0 b\u00f3ng ho\u1eb7c c\u1ea3 2 \u0111\u1ec1u l\u00e0 b\u00f3ng c\u1ee7a nhau. <\/p>\n B\u1ed9 s\u1ed1 k\u00e9p l\u1ec7ch g\u1ed3m nh\u1eefng con s\u1ed1 n\u00e0o?<\/strong> V\u1edbi c\u00e1ch soi c\u1ea7u n\u00e0y, n\u1ebfu k\u00e9p l\u1ec7ch \u0111\u01b0\u1ee3c sinh ra t\u1eeb kh\u00e1i ni\u1ec7m b\u00f3ng d\u01b0\u01a1ng th\u00ec k\u00e9p \u00e2m sinh ra t\u1eeb b\u00f3ng \u00e2m.<\/p>\n C\u00e1c c\u1eb7p b\u00f3ng \u00e2m l\u00f4 \u0111\u1ec1 bao g\u1ed3m:<\/p>\n 2 con s\u1ed1 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh l\u00e0 b\u00f3ng \u00e2m c\u1ee7a nhau khi 2 ch\u1eef s\u1ed1 t\u1ea1o n\u00ean s\u1ed1 n\u00e0y l\u00e0 b\u00f3ng \u00e2m c\u1ee7a nhau, ho\u1eb7c 2 s\u1ed1 c\u00f3 1 ch\u1eef s\u1ed1 gi\u1ed1ng nhau v\u00e0 \u0111\u1ed3ng th\u1eddi s\u1ed1 c\u00f2n l\u1ea1i l\u00e0 b\u00f3ng \u00e2m c\u1ee7a nhau. <\/p>\n T\u1eeb \u0111\u1ecbnh ngh\u0129a v\u1ec1 b\u00f3ng \u00e2m ch\u00fang ta c\u00f3 b\u1ed9 s\u1ed1 k\u00e9p \u00e2m. K\u00e9p \u00e2m l\u00e0 b\u1ed9 c\u00e1c con s\u1ed1 m\u00e0 2 ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 l\u00e0 b\u00f3ng \u00e2m c\u1ee7a nhau. B\u1ed9 k\u00e9p \u00e2m g\u1ed3m c\u00f3 c\u00e1c con s\u1ed1 sau \u0111\u00e2y: 07, 70, 14, 41, 29, 92, 36, 63, 58, 85<\/p>\n Hi\u1ec3u m\u1ed9t c\u00e1ch \u0111\u01a1n gi\u1ea3n nh\u1ea5t th\u00ec s\u00e1t k\u00e9p c\u00f3 ngh\u0129a l\u00e0 t\u1eadp h\u1ee3p nh\u1eefng con s\u1ed1 \u0111\u01b0\u1ee3c t\u1ea1o ra t\u1eeb c\u00f4ng th\u1ee9c sau: S\u00e1t k\u00e9p = S\u1ed1 k\u00e9p +\/- 1 N\u1ebfu li\u1ec7t k\u00ea b\u1ea3ng th\u1ee9 t\u1ef1 90 con s\u1ed1 c\u00f3 2 ch\u1eef s\u1ed1 ra th\u00ec s\u00e1t k\u00e9p b\u1eb1ng bao g\u1ed3m 20 con s\u1ed1 l\u00e0 nh\u1eefng s\u1ed1 n\u1eb1m li\u1ec1n k\u1ec1 v\u1edbi nh\u1eefng con s\u1ed1 n\u1eb1m trong b\u1ed9 s\u1ed1 k\u00e9p b\u1eb1ng. Chi ti\u1ebft h\u01a1n th\u00ec s\u00e1t k\u00e9p b\u1eb1ng g\u1ed3m c\u00f3 nh\u1eefng con s\u1ed1 sau \u0111\u00e2y: T\u01b0\u01a1ng t\u1ef1 nh\u01b0 tr\u00ean. B\u1ed9 s\u1ed1 s\u00e1t k\u00e9p l\u1ec7ch bao g\u1ed3m 20 s\u1ed1, l\u00e0 nh\u1eefng con s\u1ed1 s\u00e1t nh\u1ea5t, n\u1eb1m li\u1ec1n k\u1ec1 v\u1edbi c\u00e1c con s\u1ed1 trong b\u1ed9 k\u00e9p l\u1ec7ch. B\u1ed9 s\u1ed1 s\u00e1t k\u00e9p l\u1ec7ch bao g\u1ed3m nh\u1eefng con s\u1ed1 sau:
\nB\u1ed9 s\u1ed1 k\u00e9p l\u00e0 kh\u00e1i ni\u1ec7m kh\u00e1 ph\u1ed5 bi\u1ebfn trong l\u00f4 \u0111\u1ec1. Ch\u00ednh t\u00ean g\u1ecdi \u0111\u00e3 ph\u1ea3n \u00e1nh n\u00ean t\u00ednh ch\u1ea5t l\u00e0 t\u1eadp h\u1ee3p c\u1ee7a nh\u1eefng s\u1ed1 v\u1edbi 2 ch\u1eef s\u1ed1 gi\u1ed1ng h\u1ec7t nhau.
\nTuy nhi\u00ean tr\u1ea3i qua qu\u00e1 tr\u00ecnh ch\u01a1i l\u00f4 \u0111\u1ec1 v\u00e0 soi c\u1ea7u, ng\u01b0\u1eddi ta nh\u1eadn ra r\u1eb1ng c\u1ea7n m\u1edf r\u1ed9ng th\u00eam c\u00e1c b\u1ed9 s\u1ed1 k\u00e9p kh\u00e1c nhau. Ch\u00ednh v\u00ec th\u1ebf m\u00e0 xu\u1ea5t hi\u1ec7n k\u00e9p b\u1eb1ng, k\u00e9p l\u1ec7ch, s\u00e1t k\u00e9p, s\u00e1t k\u00e9p b\u1eb1ng, s\u00e1t k\u00e9p l\u1ec7ch. C\u00e1c b\u1ed9 s\u1ed1 n\u00e0y \u0111\u01b0\u1ee3c ph\u00e1t tri\u1ec3n d\u1ef1a tr\u00ean nh\u1eefng kh\u00e1i ni\u1ec7m nh\u01b0 b\u00f3ng s\u1ed1 \u0111\u1ec1.
\nV\u1eady nh\u1eefng b\u1ed9 s\u1ed1 \u0111\u00f3 kh\u00e1c nhau th\u1ebf n\u00e0o? H\u00e3y c\u00f9ng ch\u00fang t\u00f4i t\u00ecm hi\u1ec3u.<\/p>\nK\u00c9P B\u1eb0NG<\/strong><\/span><\/h3>\n
K\u00c9P L\u1ec6CH<\/strong><\/span><\/h3>\n
\nB\u00f3ng d\u01b0\u01a1ng l\u00f4 \u0111\u1ec1
\nC\u00e1c c\u1eb7p b\u00f3ng d\u01b0\u01a1ng l\u00f4 \u0111\u1ec1:<\/strong><\/p>\n\n
\nV\u00ed d\u1ee5:<\/span>
\n\u2013 C\u1eb7p s\u1ed1 43 v\u00e0 48 l\u00e0 b\u00f3ng c\u1ee7a nhau v\u00ec c\u00f9ng c\u00f3 s\u1ed1 4, b\u00ean c\u1ea1nh \u0111\u00f3 th\u00ec 3 v\u00e0 8 c\u0169ng l\u00e0 b\u00f3ng c\u1ee7a nhau.
\n\u2013 17 v\u00e0 62 l\u00e0 b\u00f3ng c\u1ee7a nhau v\u00ec 1 l\u00e0 b\u00f3ng c\u1ee7a 6 ngo\u00e0i ra th\u00ec 2 c\u0169ng l\u00e0 b\u00f3ng c\u1ee7a 7.
\n\u0110\u1ec3 d\u1ec5 hi\u1ec3u h\u01a1n v\u00e0 gi\u00fap b\u1ea1n nh\u1edb l\u00e2u h\u01a1n th\u00ec ch\u1ec9 c\u1ea7n n\u1eafm quy t\u1eafc: 2 s\u1ed1 \u0111\u01a1n v\u1ecb h\u01a1n k\u00e9m nhau 5 th\u00ec ch\u00fang l\u00e0 b\u00f3ng c\u1ee7a nhau.<\/p>\n
\nNh\u01b0 \u0111\u1ecbnh ngh\u0129a v\u1eeba n\u00eau th\u00ec nh\u1eefng s\u1ed1 l\u00e0 b\u00f3ng c\u1ee7a nhau s\u1ebd n\u1eb1m trong k\u00e9p l\u1ec7ch. V\u00ed d\u1ee5 05 l\u00e0 b\u00f3ng c\u1ee7a 00, 16 l\u00e0 b\u00f3ng c\u1ee7a 11\u2026 C\u1ee9 nh\u01b0 v\u1eady, ta x\u00e1c \u0111\u1ecbnh b\u1ed9 s\u1ed1 k\u00e9p l\u1ec7ch g\u1ed3m c\u00f3 10 s\u1ed1 nh\u01b0 sau: 05, 50, 16, 61, 27, 72, 38, 83, 49, 94<\/p>\nK\u00c9P \u00c2M<\/strong><\/span><\/h3>\n
B\u00f3ng \u00e2m<\/strong><\/h4>\n
\n
\nV\u00ed d\u1ee5:<\/span>
\n\u2013 04 v\u00e0 01 l\u00e0 b\u00f3ng \u00e2m c\u1ee7a nhau do c\u00f3 c\u00f9ng s\u1ed1 0 \u0111\u1ed3ng th\u1eddi 4 v\u00e0 1 l\u00e0 b\u00f3ng \u00e2m c\u1ee7a nhau.
\n\u2013 32 v\u00e0 96 l\u00e0 b\u00f3ng \u00e2m c\u1ee7a nhau do 3 l\u00e0 b\u00f3ng \u00e2m c\u1ee7a 6 v\u00e0 2 l\u00e0 b\u00f3ng \u00e2m c\u1ee7a 9.<\/p>\nB\u1ed9 s\u1ed1 K\u00e9p \u00e2m<\/strong><\/h4>\n
S\u00c1T K\u00c9P<\/strong><\/span><\/h3>\n
\nNh\u01b0 v\u1eady \u201cs\u00e1t k\u00e9p\u201d c\u00f3 ngh\u0129a l\u00e0 nh\u1eefng con s\u1ed1 s\u00e1t nh\u1ea5t (g\u1ea7n nh\u1ea5t) v\u1edbi s\u1ed1 k\u00e9p theo \u0111\u1ecbnh ngh\u0129a s\u01a1 kh\u1edfi nh\u1ea5t. Tuy nhi\u00ean, trong s\u00e1t k\u00e9p c\u0169ng chia ra 2 lo\u1ea1i l\u00e0 s\u00e1t k\u00e9p b\u1eb1ng v\u00e0 s\u00e1t k\u00e9p l\u1ec7ch.<\/p>\nS\u00e1t k\u00e9p b\u1eb1ng<\/strong><\/h4>\n
\n01,10,12, 21, 23, 32, 34, 43, 54, 45, 65, 56, 67, 76, 78, 87, 89, 98, 09, 90
\nL\u01b0u \u00fd:<\/span> M\u1ed9t s\u1ed1 n\u01a1i kh\u00f4ng t\u00ednh c\u1eb7p s\u1ed1 09, 90 v\u00e0o b\u1ed9 s\u00e1t k\u00e9p b\u1eb1ng. Anh em c\u1ea7n h\u1ecfi k\u1ef9 ho\u1eb7c t\u00ecm hi\u1ec3u tr\u01b0\u1edbc khi ch\u01a1i.<\/p>\nS\u00e1t k\u00e9p l\u1ec7ch<\/strong><\/h4>\n
\n04, 06, 49, 51, 15, 17, 60, 62, 26, 28, 71, 73, 37, 39, 82, 84, 48, 50, 93, 95<\/p>\n<\/div>\n
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