number of diamonds.

Algebra Level 2

7 robbers robbed a house and took away somepieces of diamonds. They stopped by a hotel for rest. While sleeping, two of the robbers woke up and decided to divide the diamons only between them and run away. While doing dat, one diamond was left so they woke the third one and started dividing but still one diamond was left. Thus they kept on waking another member and tried dividing evenlly among but every time one diamond was left. Finally they woke the seventh robber and the diamond got equally distributed. Find the number of diamonds * they robbed. * the total number of diamonds is <500.


The answer is 301.

Satish Singh by satish singh , 27, India

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2 solutions

Find the number that if divided by 2,3,4,5 and 6, the remainder is 1.
The number that can divided by 2,3,4,5 and 6 are 60, 120, 180, 240,...
So, the total number of diamonds maybe 61, 121, 181, 241, 301, ...
From this sequence, the number that can divided by 7 is 301.


1 Helpful 0 Interesting 0 Brilliant 0 Confused
Mihir Kulkarni
Jun 11, 2014

As it is only perfectly divided by 7; and reminded must be 1 when divided by number less than 7. So number must end by 1 as when divided by 5 reminder must be 1 so number must end by 6 or 1 since 6 is even and perfectly divided by 2 it is ignored. Number must end with 1 and divided by 7 when 7 is multiplied by 3,13,23,33,43... As you try to find u will get answer as 301

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