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The positive integers from 1 to 150 inclusive are placed in a 10 by 15 grid so that each cell contains exactly one integer. Then the multiples of 3 are given a red mark, the multiples of 5 are given a blue mark, and the multiples of 7 are given a green mark. How many cells have more than 1 mark?

 Nov 23, 2019
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The positive integers from 1 to 150 inclusive are placed in a 10 by 15 grid so that each cell contains exactly one integer. Then the multiples of 3 are given a red mark, the multiples of 5 are given a blue mark, and the multiples of 7 are given a green mark. How many cells have more than 1 mark?

 

This diagram is just to get you started.  Work out the very middle overlap section first. Then work out from there.

HINT: The numbers that have all 3 colours must have 3*5*7 =105 as a factor.  

 

Please no one give a full answer.

 

 Nov 23, 2019

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