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| Roulette anyone? (Posted on 2008-07-13) |
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A roulette player had a system of playing one dollar 7 times, red or black, then 7 dollars 7 times, red or black, then 49 dollars 7 times, red or black, etc., each time 7 bets in increasing powers of 7.
How many times had he won if he finally won net 777,777 dollars?
For those not familiar with the roulette, in this particular bet, if you bet 1 dollar, either you lose it or gain another 1 dollar.
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Submitted by pcbouhid
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Rating: 4.0000 (2 votes)
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Solution:
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(Hide)
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See the complete solution in the comments. Great work of Charlie and Dejmar, since a unique solution shown in the book is that with 26 winnings and 23 losses.
The book adds: "This problem is solved by expressing 777,777 as powers of 7 with odd coefficients. Then, the positive coefficients represent wins, the negative ones losses. |
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