A problem by Anjali M

Level pending

Long ago there were 7 thieves. They went to a temple to rob . With great difficulty they got a box full of gold coins. They then escaped with the loot to the woods. They tied their legs together to make sure no one takes it all for themselves. early morning one guy got up and tried to untie himself, that woke up the next person. The two of them decided to distribute the coins equally among themselves. When did so there was one coin left and so had to woke up the third person to mitigate. Now they decided to distribute among the three, but still one coin was remaining. They continued waking and redistributing, but still one coin remained all the time till all the 7 woke up. After the seventh guy also got up, the coins got distributed equally. what would be the least number of gold coins in the box?


The answer is 301.

Anjali M by Anjali M , 22

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3 solutions

Sunil Pradhan
Mar 20, 2014

No. ÷ 2, 3, 4, 5, 6 remainder 1 every time

least number = (LCM of 2, 3, 4, 5, 6) = 60 + 1 = 61 but not divisible by 7

so find multiple of 60 and add 1 that number should be divisible by 7

such number is 60 × 5 + 1 = 301

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Sharky Kesa
Jan 13, 2014

The LCM of 2,3,4,5 and 6 is 60. So, this would mean that the amount of gold coins has to be 1 greater than a multiple of 60 and also is divisible by 7. By using trial-and-error, you can work out that the answer is 301.

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Anjali M
Jan 13, 2014

1) the number should be divisible by 7 2) it should give the remainder one when divided by 2, 3, 4, 5,and 6 now the LCM of 2, 3, 4, 5, 6 is 60 so, the number of coins should be a multiple of 60 + 1 (i.e 61, 121, 181, ... )and is divisible by seven 301 happens to be the first number to meet the above.

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I can't help but notice that this problem is identical to this one. I don't mean to sound harsh, but it is blatant that you simply copied it (under a different situation). I would advise that you try to use your own creativity and come up with your own problems, and people would appreciate that much more than having a duplicate of another problem they solved earlier. :)

Brian Yao - 7 years, 5 months ago

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