[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

RES: [obm-l] Tom e jerry



á um erro na msg anterior **
Em cada rodada o gato come o **1º** rato não comido e o 13º rato não comido
1ª volta: coem os ratos 1 e 13 (pois entre o 1 e o 13 há 12 ratos)
2ª Volta: come o rato 2 aih ele conta 3-4-5-6-7-8-9-10-11-12-3-4 (come o último - 4)
3ª Volta: Come o rato 3 e conta 5-6-7-8-9-10-11-12-5-6-7-8 (come o último - 8)
acho q assim fica claro o q o gato faz.
 
[]'s MP


De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em nome de Faelccmm@aol.com
Enviada em: quarta-feira, 10 de dezembro de 2003 18:03
Para: obm-l@mat.puc-rio.br
Assunto: [obm-l] Tom e jerry

Ola pessoal,

Na resolucao da questao abaixo soh nao entendi o por que na segunda volta o gato come o rato de numero 2 e o de numero 4 ? Por que na terceira volta ele come o de numero 3 e o de numero 8 etc...   
Pela logica inicial eu pensei que teriamos os pares:
(1,13)
(2,12)
(3,11)
(4,10)
.
.
.
(6,8)
(7)

Como sobrou o 7 e este dista 6 unidades do primeiro rato da circunferencia. A resposta eh 6.
Minha solucao estaria correta se considerassemos os pares acima, mas os pares de ratos comidos sao outros. Aguardo esclarecimentos.

No mais, estah tudo entendido.


Vamos à questao:


There is a cat who just killed 13 mice. All the mice are gray but one is white. It places all the mice in a circle around it on the kitchen floor. The cat wants to eat a mouse then eat every 13th mouse ending with the white mouse. Which mouse does it start with and/or how far is this mouse from the cat?


Solution

First le't's draw a circle and numbered the mice with 1,2,3,4....13. Every time after eating a mouse, the cat will eat the 13th one which means the cat will eat 2 mice every round. after 6 rounds it will eat 12 mice. We will name the one to be the white one which is left after 6 rounds.
Place mice 1, 2,3,4,5,6,7,8,9,10,11,12,13 around a circle. The cat start to eat from mouse 1 clockwise.

first round, eat: 1st(1) and 13th(13) , left:2,3,4,5,6,7,8,9,10,11,12
second round: eat: 1st (2) and 13th (4), left : 3,5,6,7,8,9,10,11,12
third round: eat: 1st ( 3) and 13th (8), left : 5,6,7,9,10,11,12
fourth round: eat: 1st( 5) and 13th(12) , left 6,7,9,10,11
fifth round: eat: 1st( 6) and 13th( 11), left: 7,9,10
sixth round : eat 1st(7) and 13th (10) left: 9

Therefore, if the cat started to eat mouse 1 and then eat the 13th one every time, mouse 9 will be ending up to be the last one. If the cat started to eat the mouse 2, mouse 10 will be left to be the last one; if it started to eat the mouse 3, mouse 11 will be left to be the last one.

So the white mouse is 8 mice away from the one the cat started to eat clockwise.


---
Incoming mail is certified Virus Free.
Checked by AVG anti-virus system (http://www.grisoft.com).
Version: 6.0.512 / Virus Database: 309 - Release Date: 19/8/2003


---
Outgoing mail is certified Virus Free.
Checked by AVG anti-virus system (http://www.grisoft.com).
Version: 6.0.512 / Virus Database: 309 - Release Date: 19/8/2003