Dividing the Diamonds
There are seven thieves.They steal diamonds from a diamond merchant and run away in jungle. While running, night sets in and they decide to rest in the jungle.
When everybody’s sleeping, two of the best friends get up and decide to distribute the diamonds among themselves and run away. So they start distributing but find that one diamond was extra.
So they decide to wake up 3rd one and divide the diamonds again. Only to their surprise they still find one diamond extra. So they decide to wake up fourth one. Again one diamond is spare. 5th woken up…… still one extra. 6th woken up.... still one extra. Now they wake up 7th and diamonds are distributed equally.
Find the minimum number of diamonds stolen.
The answer is 301.
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1 solution
Let's represent the total diamonds to be x. It must be a multiple of 2,3,4,5 and 6 (called y) and the LCM of y = 60.
Then add 1 to 60 so 61 which is not a multiple of 7.
Keep doing this until you reach 300 + 1 = 301 mod 7 = 0.
Therefore 301.