Pirates of Caribbean
17 ' Pirates of Caribbean ' stole a sack of gold coins.They tried to distribute them equally and realized that 4 coins left.In an argument to distribute the coins,one pirate was killed.They tried to redistribute the coins and realized that 10 coins remained.Pirates again had a quarrel and one more was killed.Luckily, the coins were distributed perfectly by the remaining 15 pirates.Find the least no.of coins that could have been stolen.
The answer is 2010.
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1 solution
X = 15a = 16b + 10 = 17c + 4
X must have ended with a last digit (LD) of 5 or 0. But if we consider X = 16b + 10, X must be an even number so it's LD = 0 and b's LD = 5 or 0 AND c's LD = 8. Since X is a multiple of 3 (being a multiple of 15), then b and c cannot be a multiple of 3. c should be 1 more than a multiple of 3 while b should be 1 less than a multiple of 3.
c = { 28, 58, 88, 118, ... } = 30k – 2
b = { 5, 20, 35, 50, 65, 80, ... } = 15n – 10
16b + 10 = 17c + 4
16b = 17c – 6
= 17(30k – 2) – 6
= 510k – 40
k would need to be a multiple of 4 to match the LHS's factor of 2.
16b = 510 × 4 – 40 = 2000
b = 2000 / 16 = 125
X = 16 × 125 + 10 = 2010