# Seven thieves

Question:

There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle. 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?

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Solution: They stole 301 diamonds in total.

We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60.

60 + 1 = 61, not a multiple of 7
60 x 2 + 1 = 121, not a multiple of 7
60 x 3 + 1 = 181, not a multiple of 7
60 x 4 + 1 = 241, not a multiple of 7
60 x 5 + 1 = 301, a multiple of 7