Yancy and Zeke, two gamblers, played a series of games. The first was played for $1, the
second for $2, and so on. The stakes doubled in each successive game. After 8 games,
Yancy had won $31 more than Zeke. If no games were tied, find which games were won
by Yancy. (e.g. first, second, third)

Question

Yancy and Zeke, two gamblers, played a series of games. The first was played for $1, the
second for $2, and so on. The stakes doubled in each successive game. After 8 games,
Yancy had won $31 more than Zeke. If no games were tied, find which games were won
by Yancy. (e.g. first, second, third)

anonymous · Answer

The way I would approach the problem is to start by assuming they have won roughly the same amount of money, which means one person won the first 7 games, and the other person won the 8th.

anonymous · Answer

Then I would transferring games from the 7-game person to the 1-game person. Notice that each time I transfer a game, the score difference changes by twice the amount that particular game was worth because you're taking a victory from one person, and also giving it to the other person

anonymous · Answer

This is how I would start. |dw:1420855869621:dw| Yancy starts up by $1. Now transfer games over such that the sum of the games transferred  to yancy is 15.

anonymous · Answer

My result has Zeke winning 3 games, and Yancy winning 5 games.