A band of 17 pirates stole a sack of gold coins When they tr

A band of 17 pirates stole a sack of gold coins. When they tried to divide the fortune into equal parts, 3 coins remained. In the ensuing brawl over who should get the extra coins, one pirate was killed. The wealth was redistributed, but this time an equal division left 10 coins. Again an argument developed in which another pirate was killed. But now the total fortune was evenly distributed among the survivors. What is the least number of coins that could have been stolen?

Solution

Let the Total Coins be= x

Total pirates = 17

When the coins are divided into 17 pirates remainder left 3 coins. Hence one pirate is killed.

Again the coins are distributed among 16 pirates and remainder left 10.

And on killing one more pirate here left 15 pirates. Distribution is equal between 15 pirates.

Therefore finding a pair of numbers in which on division with 15 it will be 0 remainder and on 16 it gives 10 remainder and on 17 it gives 3.

The least number is 3930 by finding the Least Common Factor of 15,16,17 and subtracting the multiplication of maximum remainder and least number.

Hence we got the answer that is the least number of coins to be stolen are 3930 coins.