Hi\u1ec7n t\u01b0\u1ee3ng tu\u1ea7n ho\u00e0n kh\u00e1 ph\u1ed5 bi\u1ebfn trong m\u1ed9t lo\u1ea1t c\u00e1c d\u00e3y s\u1ed1, n\u1ebfu ta ch\u00fa \u00fd m\u1ed9t ch\u00fat c\u00f3 th\u1ec3 ph\u00e1t hi\u1ec7n \u0111\u01b0\u1ee3c c\u00e1c chu k\u00ec tu\u1ea7n ho\u00e0n trong c\u00e1c d\u00e3y s\u1ed1.<\/p>\n\n\n\n
V\u00ed d\u1ee5 v\u1edbi c\u00e1c lu\u1ef9 th\u1eeba c\u1ee7a c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean v\u1edbi s\u1ed1 m\u0169 l\u1edbn h\u01a1n 5, ng\u01b0\u1eddi ta th\u1ea5y c\u00f3 s\u1ef1 l\u1eb7p \u0111i l\u1eb7p l\u1ea1i ch\u1eef s\u1ed1 cu\u1ed1i. Lu\u1ef9 th\u1eeba b\u1eadc 5 c\u1ee7a 2 l\u00e0 32, ch\u1eef s\u1ed1 cu\u1ed1i c\u00f9ng l\u00e0 2, lu\u1ef9 th\u1eeba b\u1eadc 5 c\u1ee7a 3 l\u00e0 243, ch\u1eef s\u1ed1 cu\u1ed1i l\u00e0 3; lu\u1ef9 th\u1eeba b\u1eadc 5 c\u1ee7a 7, kh\u00f4ng c\u1ea7n t\u00ednh ta c\u00f3 th\u1ec3 d\u1ef1 \u0111o\u00e1n ch\u1eef s\u1ed1 cu\u1ed1i l\u00e0 7\u2026<\/p>\n\n\n\n
Quan s\u00e1t c\u00e1c ch\u1eef s\u1ed1 cu\u1ed1i c\u1ee7a c\u00e1c b\u00ecnh ph\u01b0\u01a1ng c\u00e1c s\u1ed1 t\u1eeb 1 \u0111\u1ebfn 9 ta th\u1ea5y xu\u1ea5t hi\u1ec7n d\u00e3y s\u1ed1 1, 4, 9, 6, 5, 6, 9, 4, 1. B\u00ecnh ph\u01b0\u01a1ng c\u1ee7a 10 l\u00e0 100, ch\u1eef s\u1ed1 cu\u1ed1i l\u00e0 0. C\u00e1c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a c\u00e1c s\u1ed1 ti\u1ebfp theo c\u0169ng c\u00f3 c\u00e1c ch\u1eef s\u1ed1 cu\u1ed1i l\u1eadp th\u00e0nh d\u00e3y s\u1ed1 1, 4, 9, 6, 5, 6, 9, 4, 1. T\u1ea5t c\u1ea3 c\u00e1c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 c\u00e1c ch\u1eef s\u1ed1 cu\u1ed1i l\u1eb7p \u0111i l\u1eb7p l\u1ea1i trong v\u00f2ng tu\u1ea7n ho\u00e0n n\u00e0y, hi\u1ec7n t\u01b0\u1ee3ng l\u1eb7p \u0111i l\u1eb7p l\u1ea1i v\u00f4 s\u1ed1 l\u1ea7n. V\u00f2ng l\u1eb7p \u0111i l\u1eb7p l\u1ea1i n\u00e0y c\u00f3 s\u1ed1 0 l\u00e0m ranh gi\u1edbi.<\/p>\n\n\n\n
Ng\u01b0\u1eddi ta c\u00f2n ph\u00e1t hi\u1ec7n \u201cs\u1ed1 g\u1ed1c\u201d c\u1ee7a c\u00e1c b\u00ecnh ph\u01b0\u01a1ng ch\u1ec9 c\u00f3 th\u1ec3 l\u00e0 1, 4, 7, 9 m\u00e0 kh\u00f4ng th\u1ec3 l\u00e0 c\u00e1c ch\u1eef s\u1ed1 kh\u00e1c. Ng\u01b0\u1eddi ta g\u1ecdi \u201cs\u1ed1 g\u1ed1c\u201d c\u1ee7a m\u1ed9t s\u1ed1 l\u00e0 ch\u1ec9 con s\u1ed1 thu \u0111\u01b0\u1ee3c khi c\u1ed9ng d\u1ea7n c\u00e1c ch\u1eef s\u1ed1 c\u00f3 trong con s\u1ed1, khi t\u1ed5ng s\u1ed1 g\u1eb7p s\u1ed1 9 th\u00ec b\u1ecf \u0111i v\u00e0 t\u00ednh t\u1ed5ng ti\u1ebfp n\u1ebfu g\u1eb7p s\u1ed1 9 l\u1ea1i b\u1ecf \u0111i \u0111\u1ebfn khi c\u00f2n l\u1ea1i s\u1ed1 cu\u1ed1i c\u00f9ng nh\u1ecf h\u01a1n 9 th\u00ec gi\u1eef l\u1ea1i, ch\u1eef s\u1ed1 c\u00f2n l\u1ea1i l\u00e0 \u201cs\u1ed1 g\u1ed1c\u201d c\u1ee7a con s\u1ed1 \u0111\u00e3 x\u00e9t. Nh\u01b0 v\u1eady \u201cs\u1ed1 g\u1ed1c\u201d ch\u00ednh l\u00e0 k\u1ebft qu\u1ea3 ph\u00e9p t\u00ednh c\u1ed9ng d\u1ed3n c\u00e1c ch\u1eef s\u1ed1 c\u00f3 trong m\u1ed9t con s\u1ed1, l\u1ea5y s\u1ed1 9 l\u00e0m \u0111i\u1ec3m d\u1eebng. V\u00ed d\u1ee5 \u201cs\u1ed1 g\u1ed1c\u201d c\u1ee7a 135 l\u00e0 9, s\u1ed1 g\u1ed1c c\u1ee7a s\u1ed1 246 l\u00e0 3\u2026<\/p>\n\n\n\n
\u1ee8ng d\u1ee5ng t\u00ednh ch\u1ea5t v\u1eeba n\u00eau ta c\u00f3 th\u1ec3 ph\u00e1n \u0111o\u00e1n m\u1ed9t s\u1ed1 c\u00f3 ph\u1ea3i l\u00e0 m\u1ed9t s\u1ed1 ch\u00ednh ph\u01b0\u01a1ng (b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t s\u1ed1 n\u00e0o \u0111\u00f3) hay kh\u00f4ng. V\u00ed d\u1ee5 x\u00e9t xem s\u1ed1 98765432123456789 c\u00f3 ph\u1ea3i l\u00e0 m\u1ed9t ch\u00ednh ph\u01b0\u01a1ng hay kh\u00f4ng? Ta t\u00ecm s\u1ed1 g\u1ed1c c\u1ee7a con s\u1ed1 v\u1eeba \u0111\u01b0a ra v\u00e0 th\u1ea5y s\u1ed1 \u0111\u00f3 c\u00f3 s\u1ed1 g\u1ed1c l\u00e0 8 m\u00e0 kh\u00f4ng ph\u1ea3i l\u00e0 m\u1ed9t trong c\u00e1c ch\u1eef s\u1ed1 1, 4, 7, 9. V\u1eady con s\u1ed1 v\u1eeba n\u00eau kh\u00f4ng ph\u1ea3i l\u00e0 s\u1ed1 ch\u00ednh ph\u01b0\u01a1ng.<\/p>\n\n\n\n
S\u1ed1 g\u1ed1c c\u1ee7a m\u1ed9t ch\u00ednh ph\u01b0\u01a1ng kh\u00f4ng ch\u1ec9 c\u00f3 \u0111\u1eb7c t\u00ednh v\u1eeba n\u00eau m\u00e0 c\u00f2n th\u00e0nh l\u1eadp d\u00e3y s\u1ed1 tu\u1ea7n ho\u00e0n 1, 4, 9, 7, 7, 9, 4, 1. \u1ede \u0111\u00e2y ch\u1eef s\u1ed1 ranh gi\u1edbi l\u00e0 9 ch\u1ee9 kh\u00f4ng ph\u1ea3i s\u1ed1 0 nh\u01b0 \u1edf c\u00e1c chu k\u00ec kh\u00e1c. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t d\u00e3y l\u00e0m v\u00ed d\u1ee5: 100 (b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a s\u1ed1 10) c\u00f3 s\u1ed1 g\u1ed1c l\u00e0 1. 121 (b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a s\u1ed1 11) c\u00f3 s\u1ed1 g\u1ed1c l\u00e0 4. 144 (b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a s\u1ed1 12) c\u00f3 s\u1ed1 g\u1ed1c l\u00e0 9. 169 (b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a s\u1ed1 13) c\u00f3 s\u1ed1 g\u1ed1c l\u00e0 7. 196 (b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a s\u1ed1 14) c\u00f3 s\u1ed1 g\u1ed1c l\u00e0 7. 225 (b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a s\u1ed1 15) c\u00f3 s\u1ed1 g\u1ed1c l\u00e0 9. 256 (b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a s\u1ed1 16) c\u00f3 s\u1ed1 g\u1ed1c l\u00e0 4. 324 (b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a s\u1ed1 18) c\u00f3 s\u1ed1 g\u1ed1c l\u00e0 9 (ranh gi\u1edbi c\u1ee7a chu k\u00ec). 361 (b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a s\u1ed1 19) c\u00f3 s\u1ed1 g\u1ed1c l\u00e0 1 (chu k\u00ec l\u1eb7p l\u1ea1i).<\/p>\n\n\n\n
T\u00ednh ch\u1ea5t n\u00e0y c\u1ee7a c\u00e1c b\u00ecnh ph\u01b0\u01a1ng kh\u00f4ng ch\u1ec9 r\u1ea5t th\u00fa v\u1ecb m\u00e0 c\u00f3 gi\u00e1 tr\u1ecb th\u1ef1c ti\u1ec5n l\u1edbn. V\u1eadn d\u1ee5ng linh ho\u1ea1t t\u00ednh ch\u1ea5t n\u00e0y c\u00f3 th\u1ec3 n\u1eafm ch\u1eafc \u0111\u01b0\u1ee3c c\u00e1c m\u1eb9o nh\u1ecf trong t\u00ednh to\u00e1n nhanh.<\/p>\n\n\n\n
T\u1eeb kho\u00e1: T\u00ednh tu\u1ea7n ho\u00e0n trong c\u00e1c b\u00ecnh ph\u01b0\u01a1ng.<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Hi\u1ec7n t\u01b0\u1ee3ng tu\u1ea7n ho\u00e0n kh\u00e1 ph\u1ed5 bi\u1ebfn trong m\u1ed9t lo\u1ea1t c\u00e1c d\u00e3y s\u1ed1, n\u1ebfu ta ch\u00fa \u00fd m\u1ed9t ch\u00fat c\u00f3 th\u1ec3 ph\u00e1t hi\u1ec7n \u0111\u01b0\u1ee3c c\u00e1c chu k\u00ec tu\u1ea7n ho\u00e0n trong c\u00e1c d\u00e3y s\u1ed1. V\u00ed d\u1ee5 v\u1edbi c\u00e1c lu\u1ef9 th\u1eeba c\u1ee7a c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean v\u1edbi s\u1ed1 m\u0169 l\u1edbn h\u01a1n 5, ng\u01b0\u1eddi ta th\u1ea5y c\u00f3 s\u1ef1 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[15,9],"tags":[],"class_list":["post-7495","post","type-post","status-publish","format-standard","hentry","category-hoi-dap-khoa-hoc","category-toan-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7495","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=7495"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7495\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7495"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7495"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7495"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}