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?

Guest Nov 23, 2019

#1**+1 **

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.**

Melody Nov 23, 2019