6. [Bonus question: 4 bonus marks A family has five children aged 7, 8, 9, 10, 1

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6. [Bonus question: 4 bonus marks A family has five children aged 7, 8, 9, 10, 11. On a shelf in the family room there is a piggy bank into which their parents put any one- dollar coins (and only one-dollar coins) on hand at the end of the work week. After a long time wondering how to get the money out of that piggy bank, one dav the children figure it out and get 57 one-dollar coins They decide that, since they collectively stole the money, they should collectively decide how to split it up. (Maybe a collective punishment will be less severe.) They decide that: The youngest child in the group will suggest how to divide the money, and then all members of the group will vote on it. If the at least half of the members of group support the suggestion, then coins will be divided in that way. Otherwise, the proposer is eliminated from consideration and the coins are divided among the smaller group according to the same procedure Each child knows their siblings will not support any suggestion if they could get more coins later in the process by waiting. Also, each child knows their siblings will not support any suggestion under which they could get the same number of coins later because it means their sibling gets nothing What is the maximum amount of money the youngest child can get? Explain

Explanation / Answer

Anything the youngest guy say, there is a big chance that the suggestion will not be considered.

So in order to get some money, he can suggest that the amount of money should be distributed among them according to their ages. The amont will be the same as their age.

The oldest guy must be agree and if the other people wont agree then they would get the amont same as their age as this is the suggestion and they have to follow the same and it will not change the amount of money they will get.

So in any scenerio the max amount of money the youngest guy can get is 7.

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