There are 50 citizens in Timmyville, including King Timmy. Each person has a sal

Question

There are 50 citizens in Timmyville, including King Timmy. Each person has a salary of $1. Each persons salary must be a non-negative integer number of dollars. The king may make a suggestion as to how to distrubute the $50 for salaries. Then a vote is held. A citizn will vote "no" if the suggestions lower his/her salary and "yes" if the suggestion will raise his/her salary. IF no change occcurs, the citizen will abstain. IF there are strictly more"yes" votes than "no" votes then the suggestion passes into law. Of timmy can make as many suggestions as he likes, then what is the largest salary Timmy can acheive if...

1) Timmy is allowed to vote (in which case, he can vote however he likes).

2)Tmmy is not allow to vote

Explanation / Answer

24 go to 0, 25 go to 2 and king timmy goes to 0. 25 yes beats 24 no.

Then of these 25, send 12 to 0 and 13 to 3. timmy gets the 11 left. 13 yes beats 12 no. Rest abstain.

Then of these 13, send 6 to 0 and 7 to 4. timmy gets the 22 left.

THen of these 7, send 3 to 0 and 4 to 5. timmy gets the 30 left.

Then of these 4, send 2 to 0 and 2 to 6. timmy votes yes and gets the 38 left over.

Then of these 2 send 1 to 0 and the other to 7. timmy votes yes and gets the other 43. There is no way to get this guy to decrease his salary.

If timmy cannot vote, then everything is the same until there are 4 people left. Then 1 goes to 0, 1 stays at 5, and the other 2 go to 6. Timmy gets the 33 left.

Then 1 of the $6 people goes to 0, the other two increase to 6 and 7 respectively. Timmy gets the remaining 37.

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