How many diamonds did they steal in total?

Question

7 thieves rob a diamond merchant of some diamonds.

They return to their den and go off to sleep.

When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves.

But when they divided the diamonds equally, one diamond is left.

So they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left.

Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left.

This happened with the 5th and 6th thief – one diamond was still left.
Finally, they woke up the 7th thief and this time the diamonds were divided equally.

How many diamonds did they steal in total?

Answer 1

301 diamonds

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The number should be divisible by 7 and leave reminder of 1 when divided by 2,3,4,5,6. LCM of 2,3,4,5,6= 60, the number can be found by the formula: 7x=60y+1. By trying y from 1 to 12 we get a smallest number of 301 (y=5), the next one is 721 (y=12) etc. in general it would be 7x=60*(5+7n)+1, where n>=0