[obm-l] Tom e jerry

[Faelccmm@xxxxxxx]

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.