A Dice Bet

The point is to read carefully. There are SEVEN dice, and a dice has only 6 sides. Therefore, even thought it will take Mary a long time, she is sure to win, because it's IMPOSSIBLE to throw all the seven dice differently.

It is pretty obvious that you can't roll 7 different numbers between 1 and 6. Thus it is impossible for Jhon to win. Therefor Mary is bound to win eventually.

A dice has only six faces, so how can the seven dices will attain seven different scores??

This is a tricky one. If there are 7 dices, they can't be all different.

John will never win because in order to win, John must roll all dice showing all different numbers but a regular die only has 6 sides. Therefore, the probability that Mary will win which is $7/{279936}$ is higher than the probability that John will win which is $0$ .

7 different landings are not possible. so, only mary will win.

There are 6 possibilities for each die and there are 7 dice..S all the dice cannot come up differently....So John can never win...So after some time Mary will win...

because if we have 7 dice then it is definite to repeat one number atleast . So marry will win.

1/46656 chance 3_3

There are seven dice. Therefore, not all of them can be different, and thus Mary wins.

This is a good example of the pigeon hole principle.

Let's say the first six people each rolled something different; the seventh person, whatever he or she rolls, will repeat one of the results that the other six got because a die only has SIX possible outcomes and there are SEVEN people.

So even though Mary's conditions are hard to meet, John's are IMPOSSIBLE.

What was the name of the murderous math book of yours

a dice have only 6 sides so 7 different side is not possible but same 7 sides is possible.so mary is sure to win

How can seven dices show differently if they have only six sides? So Its Impossible for John to win.

awesome!

Impossible for John to throw the die differently seven times. :D

simple,the dice have six different faces and seven dices cannot be fully different,atleast two shall carry the same no.

There are 7 dice and each has 6 faces so John can never win since at the least two dice will have same value.On the other hand Mary has probability of 1/46656 of getting the same value in all the dice. So Mary has the chances of winning.

Com 7 dados... João não consegue ganhar porque sempre terá um dado igual

Since John gets different nos on dice,but each dice has six only,7th can not be different.With minimum different nos and 7th dice max 6 taken will make it total 27. While mary b can get gigher nos starting from 4,5 & 6. So Mary is sure to win

K.K.GARG,India

Becoz there are six faces in a dice.. so seven different outcomes is not not possible

As there are 7 dice and each dice has only six different faces it is impossible to get different faces at the same time i.e. at least two dice have same faces at the same time.(pigeonhole's principle)

There are only 6 faces on a cube, so to have 7 different number is impossible. marry may be win but john has no probability .

A dice has six faces and hence at max six different outcomes. If there are seven dice, then it is sure that at least two dice will have the same number...

By using Pigeon Hole Principle it is clear that there can't be 7 different outcomes on a six sided dice........... so surely John can't win therefore Mary will win for sure

Mary is the only person who can win the game. John can never win as throwing seven different digits with only six is impossible.

P(all seven dice have same number) = 6/6^7

P(all seven dice have diff number)= 0 because dice have only six faces and for seven dice at least 2 dice have same number on their faces. So all 7 with diff numbers is not possible.

Hence Mary is sure to win.

no matter how many times the dice is thrown at least two dice will show the same good question.