87. The Thieves and the Gold Coins
Four thieves steal some gold coins from the palace. It was decided to gather at the appointed place and distribute coins in the morning.
At night a thief gets up and divides the stolen coin into four equal parts. One coin remains, he throws it away. He keeps one part out of four and keeps the remaining three parts in a basket.
After a while, another thief divides the coin into four equal parts, leaving one coin left. He throws it away. He keeps one part out of four and keeps the remaining three parts in a basket.
Sometimes a third thief divides the coin into four equal parts, leaving a coin left, and he throws it away. He keeps one part out of four and keeps the remaining three parts in a basket.
Then the fourth thief divides the coin into four equal parts, leaving one coin left, and he throws it away. He keeps one part out of four and keeps the remaining three parts in a basket.
In the morning, the coins in the pot are divided into four equal parts as per the schedule.
Added 28 April 2020
Solution:
Originally stolen coins: 765.
Night divisions: 1) First thief discards 1, takes 191, leaves 573. 2) Second thief discards 1, takes 143, leaves 429. 3) Third thief discards 1, takes 107, leaves 321. 4) Fourth thief discards 1, takes 80, leaves 240.
Morning division: 240 coins ÷ 4 = 60 each.
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