{"id":7567,"date":"2021-11-20T14:03:34","date_gmt":"2021-11-20T07:03:34","guid":{"rendered":"https:\/\/www.vietlearn.org\/post\/?p=7567"},"modified":"2021-11-20T17:13:36","modified_gmt":"2021-11-20T10:13:36","slug":"trong-mot-buoi-len-lop-thay-giao-da-dua-ra-cho-hoc-sinh-mot-de-toan-sau-day-tren-mot-chiec-thuyen-co-75-con-trau-32-con-de-hoi-thuyen-truong-bao-nhieu-tuoi","status":"publish","type":"post","link":"https:\/\/www.vietlearn.org\/kien-thuc\/trong-mot-buoi-len-lop-thay-giao-da-dua-ra-cho-hoc-sinh-mot-de-toan-sau-day-tren-mot-chiec-thuyen-co-75-con-trau-32-con-de-hoi-thuyen-truong-bao-nhieu-tuoi\/","title":{"rendered":"Trong m\u1ed9t bu\u1ed5i l\u00ean l\u1edbp, th\u1ea7y gi\u00e1o \u0111\u00e3 \u0111\u01b0a ra cho h\u1ecdc sinh m\u1ed9t \u0111\u1ec1 to\u00e1n sau \u0111\u00e2y: Tr\u00ean m\u1ed9t chi\u1ebfc thuy\u1ec1n c\u00f3 75 con tr\u00e2u, 32 con d\u00ea, h\u1ecfi thuy\u1ec1n tr\u01b0\u1edfng bao nhi\u00eau tu\u1ed5i."},"content":{"rendered":"\n<p>M\u1ea5y ph\u00fat sau, c\u00e1c <a href=\"https:\/\/www.vietlearn.org\" data-internallinksmanager029f6b8e52c=\"2\" title=\"Vietlearn\" rel=\"nofollow\">h\u1ecdc sinh<\/a> \u0111\u00e3 l\u00e0m xong. Th\u1ea7y gi\u00e1o y\u00eau c\u1ea7u b\u00e9 Hoa \u0111\u01b0a ra l\u1eddi gi\u1ea3i c\u1ee7a m\u00ecnh, b\u1ea1n Hoa tr\u1ea3 l\u1eddi \u201cThuy\u1ec1n tr\u01b0\u1edfng 43 tu\u1ed5i\u201d. Th\u1ea7y gi\u00e1o l\u1ea1i g\u1ecdi b\u1ea1n L\u00e2m n\u00f3i k\u1ebft qu\u1ea3, b\u1ea1n L\u00e2m tr\u1ea3 l\u1eddi \u201cThuy\u1ec1n tr\u01b0\u1edfng 53,5 tu\u1ed5i\u201d. Nghe hai c\u00e2u tr\u1ea3 l\u1eddi, b\u1ea1n D\u0169ng n\u00f3i \u201cB\u00e0i to\u00e1n n\u00e0y kh\u00f4ng gi\u1ea3i \u0111\u01b0\u1ee3c\u201d. C\u00e1c b\u1ea1n ngh\u0129 xem trong ba b\u1ea1n <a href=\"https:\/\/www.vietlearn.org\" data-internallinksmanager029f6b8e52c=\"2\" title=\"Vietlearn\" rel=\"nofollow\">h\u1ecdc sinh<\/a>, b\u1ea1n n\u00e0o \u0111\u00e3 n\u00f3i \u0111\u00fang?<\/p>\n\n\n\n<p>S\u1ef1 th\u1ef1c th\u00ec s\u1ed1 tu\u1ed5i c\u1ee7a thuy\u1ec1n tr\u01b0\u1edfng kh\u00f4ng h\u1ec1 c\u00f3 m\u1ed1i li\u00ean quan n\u00e0o v\u1edbi s\u1ed1 tr\u00e2u, d\u00ea tr\u00ean thuy\u1ec1n. V\u00ec th\u1ebf t\u1eeb 75 con tr\u00e2u v\u00e0 32 con d\u00ea kh\u00f4ng th\u1ec3 n\u00e0o t\u00ednh \u0111\u01b0\u1ee3c tu\u1ed5i c\u1ee7a thuy\u1ec1n tr\u01b0\u1edfng.<\/p>\n\n\n\n<p>Th\u1ebf t\u1ea1i sao b\u1ea1n Hoa v\u00e0 b\u1ea1n L\u00e2m \u0111\u1ec1u \u0111\u01b0a ra l\u1eddi gi\u1ea3i \u0111\u00e1p cho m\u1ed9t b\u00e0i to\u00e1n kh\u00f4ng c\u00f3 l\u1eddi gi\u1ea3i. Nguy\u00ean do l\u00e0 c\u00e1c em c\u0169ng ngh\u0129 \u0111\u1ebfn vi\u1ec7c b\u00e0i to\u00e1n kh\u00f4ng c\u00f3 l\u1eddi gi\u1ea3i nh\u01b0ng l\u1ea1i ngh\u0129 r\u1eb1ng ph\u00e0m th\u1ea7y gi\u00e1o \u0111\u00e3 ra \u0111\u1ec1 l\u1ebd n\u00e0o l\u1ea1i l\u00e0 b\u00e0i to\u00e1n kh\u00f4ng c\u00f3 l\u1eddi gi\u1ea3i. V\u00ec th\u1ebf b\u00e9 Hoa \u0111\u00e3 gi\u1ea3m b\u1edbt con s\u1ed1 l\u1edbn c\u00f2n b\u1ea1n L\u00e2m l\u1ea1i l\u1ea5y trung b\u00ecnh c\u1ee7a hai s\u1ed1 l\u00e0m l\u1eddi gi\u1ea3i.<\/p>\n\n\n\n<p>Trong cu\u1ed9c thi Olympic to\u00e1n qu\u1ed1c t\u1ebf n\u0103m 1947 \u1edf Hungari c\u00f3 m\u1ed9t b\u00e0i to\u00e1n nh\u01b0 sau: Ch\u1ee9ng minh r\u1eb1ng trong m\u1ed9t nh\u00f3m s\u00e1u ng\u01b0\u1eddi b\u1ea5t k\u00ec \u00edt nh\u1ea5t c\u00f3 ba \u0111\u00e3 t\u1eebng b\u1eaft tay nhau ho\u1eb7c \u00edt nh\u1ea5t c\u00f3 ba ng\u01b0\u1eddi ch\u01b0a t\u1eebng b\u1eaft tay nhau\u201d. Th\u00e1ng 6-1956 m\u1ed9t t\u1edd nguy\u1ec7t san to\u00e1n c\u1ee7a M\u1ef9 \u0111\u00e3 chuy\u1ec3n m\u1ec7nh \u0111\u1ec1 n\u00e0y th\u00e0nh m\u1ed9t tr\u00f2 ch\u01a1i to\u00e1n h\u1ecdc, t\u1eeb \u0111\u00f3 hai b\u00e0i to\u00e1n tr\u1edf th\u00e0nh m\u1ed9t \u0111\u1ec1 to\u00e1n l\u00ed th\u00fa m\u00e0 ng\u01b0\u1eddi ta th\u01b0\u1eddng g\u1ecdi l\u00e0 \u201cb\u00e0i to\u00e1n nh\u00f3m s\u00e1u ng\u01b0\u1eddi\u201d.<\/p>\n\n\n\n<p>L\u00e0m th\u1ebf n\u00e0o ch\u1ee9ng minh m\u1ec7nh \u0111\u1ec1 \u0111\u00f3? Tr\u01b0\u1edbc h\u1ebft ta c\u00f3 th\u1ec3 s\u1eafp x\u1ebfp nh\u00f3m s\u00e1u ng\u01b0\u1eddi b\u1ea5t k\u00ec n\u00e0y tr\u00ean s\u00e1u \u0111i\u1ec3m \u0111\u1ec9nh kh\u00e1c nhau v\u00e0 \u0111\u1ea1i di\u1ec7n b\u1eb1ng c\u00e1c ch\u1eef c\u00e1i A, B, C, D, E, F, d\u00f9ng c\u00e1c n\u00e9t li\u1ec1n \u0111\u1ec3 n\u1ed1i c\u00e1c \u0111\u1ec9nh bi\u1ec3u di\u1ec5n l\u00e0 ng\u01b0\u1eddi b\u1eaft tay nhau, v\u00e0 d\u00f9ng n\u00e9t \u0111\u1ee9t \u0111\u1ec3 bi\u1ec3u di\u1ec5n vi\u1ec7c hai ng\u01b0\u1eddi ch\u01b0a h\u1ec1 b\u1eaft tay nhau. Nh\u1edd \u0111\u00f3 ta bi\u1ec3u di\u1ec5n \u0111\u01b0\u1ee3c tr\u1ea1ng th\u00e1i b\u1eaft tay (v\u00e0 kh\u00f4ng b\u1eaft tay nhau) c\u1ee7a nh\u00f3m s\u00e1u ng\u01b0\u1eddi th\u00e0nh gi\u1ea3n \u0111\u1ed3. Tr\u00ean h\u00ecnh 1 m\u00f4 t\u1ea3 tr\u1ea1ng th\u00e1i b\u1eaft tay c\u1ee7a s\u00e1u ng\u01b0\u1eddi.<\/p>\n\n\n\n<p>Theo nh\u01b0 h\u00ecnh 1 c\u00f3 bao nhi\u00eau tr\u1ea1ng th\u00e1i? Trong m\u1ed7i quan h\u1ec7 b\u1eaft tay nhau, t\u1eeb m\u1ed7i \u0111i\u1ec3m \u0111\u1ec9nh c\u00f3 th\u1ec3 v\u1ebd 5 \u0111\u01b0\u1eddng th\u1eb3ng n\u1ed1i li\u1ec1n v\u1edbi c\u00e1c \u0111\u1ec9nh kh\u00e1c t\u1ee9c l\u00e0 6 x 5 = 30 c\u1ea1nh, nh\u01b0ng trong \u0111\u00f3 c\u00f3 m\u1ed9t n\u1eeda l\u00e0 tr\u00f9ng nhau. V\u00e0 nh\u01b0 v\u1eady tr\u1ea1ng th\u00e1i b\u1eaft tay nhau c\u00f3 30 : 2 = 15 c\u1ea1nh, m\u1ed7i c\u1ea1nh l\u1ea1i c\u00f3 hai lo\u1ea1i n\u00e9t li\u1ec1n v\u00e0 n\u00e9t \u0111\u1ee9t v\u00e0 nh\u01b0 v\u1eady trong m\u1ed1i quan h\u1ec7 b\u1eaft tay nhau c\u1ee7a s\u00e1u ng\u01b0\u1eddi c\u00f3 215 t\u00ecnh hu\u1ed1ng kh\u00e1c nhau. D\u01b0\u1edbi \u0111\u00e2y ta s\u1ebd ch\u1ee9ng minh lu\u1eadn \u0111\u1ec1 n\u00eau tr\u00ean.<\/p>\n\n\n\n<p>Tr\u01b0\u1edbc h\u1ebft ta x\u00e9t m\u1ed9t \u0111i\u1ec3m \u0111\u1ec9nh nh\u01b0 A ch\u1eb3ng h\u1ea1n \u00edt nh\u1ea5t c\u00f3 th\u1ec3 b\u1eaft tay v\u1edbi ba ng\u01b0\u1eddi, v\u00e0 \u00edt nh\u1ea5t c\u0169ng c\u00f3 ba ng\u01b0\u1eddi kh\u00f4ng b\u1eaft tay v\u1edbi A. C\u0169ng t\u01b0\u01a1ng t\u1ef1 ta s\u1ebd t\u00ecm th\u1ea5y tr\u1ea1ng th\u00e1i kh\u00f4ng b\u1eaft tay c\u1ee7a A v\u1edbi ba ng\u01b0\u1eddi. Tr\u01b0\u1edbc h\u1ebft ta x\u00e9t t\u00ecnh hu\u1ed1ng 1, \u00edt nh\u1ea5t c\u00f3 ba ng\u01b0\u1eddi b\u1eaft tay v\u1edbi A.<\/p>\n\n\n\n<p>V\u00ed d\u1ee5 B, C, D ch\u1eb3ng h\u1ea1n. Nh\u01b0 t\u00ecnh hu\u1ed1ng \u1edf h\u00ecnh 2 bi\u1ec3u di\u1ec5n \u00edt nh\u1ea5t c\u00f3 ba ng\u01b0\u1eddi B, C, D ch\u01b0a b\u1eaft tay v\u1edbi A (\u0111\u01b0\u1eddng n\u1ed1i l\u00e0 n\u00e9t \u0111\u1ee9t), n\u1ebfu kh\u00f4ng s\u1ed1 ng\u01b0\u1eddi b\u1eaft tay v\u00e0 kh\u00f4ng b\u1eaft tay nhau s\u1ebd nh\u1ecf h\u01a1n 5.<\/p>\n\n\n\n<p>Tr\u01b0\u1edbc h\u1ebft ta x\u00e9t t\u00ecnh hu\u1ed1ng 1 trong tr\u1ea1ng th\u00e1i n\u00e0y. A \u00edt nh\u1ea5t b\u1eaft tay v\u1edbi ba ng\u01b0\u1eddi v\u00ed d\u1ee5 v\u1edbi B, C, D ch\u1eb3ng h\u1ea1n. N\u1ebfu B, C, D l\u00e0 ba ng\u01b0\u1eddi ch\u01b0a h\u1ec1 b\u1eaft tay nhau (h\u00ecnh 2) n\u00ean \u0111\u00e2y l\u00e0 t\u00ecnh hu\u1ed1ng c\u00f3 ng\u01b0\u1eddi ch\u01b0a h\u1ec1 b\u1eaft tay nhau. N\u1ebfu kh\u00f4ng, trong ba ng\u01b0\u1eddi \u00edt nh\u1ea5t c\u00f3 hai ng\u01b0\u1eddi b\u1eaft tay nhau, v\u00ed d\u1ee5 gi\u1eefa C v\u00e0 D (h\u00ecnh 3) nh\u01b0 v\u1eady \u0111\u00e3 \u0111\u00e1p \u1ee9ng v\u1edbi m\u1ec7nh \u0111\u1ec1 \u00edt nh\u1ea5t c\u00f3 ba ng\u01b0\u1eddi b\u1eaft tay nhau. Ta h\u00e3y x\u00e9t lo\u1ea1i t\u00ecnh hu\u1ed1ng th\u1ee9 hai, \u00edt nh\u1ea5t A ch\u01b0a h\u1ec1 b\u1eaft tay v\u1edbi ba ng\u01b0\u1eddi kh\u00e1c, gi\u1ea3 s\u1eed v\u1edbi B, C, D; b\u1ea5y gi\u1edd ta ch\u1ec9 c\u1ea7n thay n\u00e9t li\u1ec1n th\u00e0nh n\u00e9t \u0111\u1ee9t tr\u00ean h\u00ecnh 2. C\u00e1c ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1, c\u00e1c b\u1ea1n c\u00f3 th\u1ec3 t\u1ef1 ti\u1ebfp t\u1ee5c v\u00e0 s\u1ebd t\u00ecm \u0111\u01b0\u1ee3c k\u1ebft lu\u1eadn c\u1ea7n thi\u1ebft. T\u1eeb c\u00e1c l\u00ed lu\u1eadn tr\u00ean \u0111\u00e2y ch\u00fang ta c\u00f3 th\u1ec3 ch\u1ee9ng minh, trong nh\u00f3m s\u00e1u ng\u01b0\u1eddi b\u1ea5t k\u00ec, \u00edt nh\u1ea5t c\u00f3 ba ng\u01b0\u1eddi b\u1eaft tay nhau ho\u1eb7c \u00edt nh\u1ea5t c\u00f3 ba ng\u01b0\u1eddi ch\u01b0a h\u1ec1 b\u1eaft tay nhau.<\/p>\n\n\n\n<p>Ng\u01b0\u1eddi ta c\u00f3 th\u1ec3 ti\u1ebfn th\u00eam m\u1ed9t b\u01b0\u1edbc n\u1eefa, trong nh\u00f3m c\u00f3 s\u00e1u ng\u01b0\u1eddi \u00edt nh\u1ea5t c\u00f3 ba ng\u01b0\u1eddi t\u1eebng b\u1eaft tay nhau, ho\u1eb7c \u00edt nh\u1ea5t ba ng\u01b0\u1eddi ch\u01b0a h\u1ec1 b\u1eaft tay nhau. Th\u1ebf nh\u01b0ng n\u1ebfu s\u1ed1 ng\u01b0\u1eddi \u00edt h\u01a1n s\u00e1u th\u00ec k\u1ebft lu\u1eadn s\u1ebd kh\u00f4ng ph\u00f9 h\u1ee3p. H\u00ecnh 4 bi\u1ec3u di\u1ec5n \u0111i\u1ec1u \u0111\u00f3: trong nh\u00f3m s\u00e1u ng\u01b0\u1eddi kh\u00f4ng c\u00f3 ba ng\u01b0\u1eddi \u0111\u00e3 b\u1eaft tay nhau, c\u0169ng kh\u00f4ng c\u00f3 ba ng\u01b0\u1eddi ch\u01b0a h\u1ec1 b\u1eaft tay nhau.<\/p>\n\n\n\n<p>T\u1eeb kho\u00e1: B\u00e0i to\u00e1n nh\u00f3m s\u00e1u ng\u01b0\u1eddi.<\/p>\n\n\n\n<p><\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"<p>M\u1ea5y ph\u00fat sau, c\u00e1c h\u1ecdc sinh \u0111\u00e3 l\u00e0m xong. Th\u1ea7y gi\u00e1o y\u00eau c\u1ea7u b\u00e9 Hoa \u0111\u01b0a ra l\u1eddi gi\u1ea3i c\u1ee7a m\u00ecnh, b\u1ea1n Hoa tr\u1ea3 l\u1eddi \u201cThuy\u1ec1n tr\u01b0\u1edfng 43 tu\u1ed5i\u201d. Th\u1ea7y gi\u00e1o l\u1ea1i g\u1ecdi b\u1ea1n L\u00e2m n\u00f3i k\u1ebft qu\u1ea3, b\u1ea1n L\u00e2m tr\u1ea3 l\u1eddi \u201cThuy\u1ec1n tr\u01b0\u1edfng 53,5 tu\u1ed5i\u201d. Nghe hai c\u00e2u tr\u1ea3 l\u1eddi, b\u1ea1n D\u0169ng n\u00f3i \u201cB\u00e0i [&hellip;]<\/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-7567","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\/7567","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=7567"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7567\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7567"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7567"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7567"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}