Fair
Division?
Late one night five thieves stole a bag of coins. When
they returned to their hideout they were all very tired and decided to
go to sleep leaving the division of the coins until morning.
Then in the middle of the night...
| Thief 1 woke up
|
Thief 2 later in the night
|
|---|
And so it continued through the night; thief 3 woke up and divided the money into 5 piles, he had one coin left so he added it to the pile that he took for his own. Later thief 4 woke, divided the coins into 5 piles, he also had one coin left which he slipped into his pocket while taking one of the piles. The last thief woke, split the remaining coins into 5 piles with one coin left over. He took the extra coin and one of the piles.
When morning came the 5 thieves gathered around the coins and counted them out into 5 equal piles with no coins remaining. What is the smallest number of coins that could have been in the bag of stolen coins?
Extention: What is the smallest number of coins in the bag if we know
that there were at least 10,000 coins?
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Sample of correct solutions for this problem will be posted after June 13, 1997.
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2 June, 1997
