Numbers and boxes

Probability Level 4

The integers from 1 to 1000 (inclusive) are to be placed into boxes such that no box contains a number that is a multiple of another number in the same box.

What is the minimum number of boxes needed?


As an explicit example, the integers from 1 to 10 can be placed into 4 boxes while satisfying the condition:

  • Box 1 - {1} \{ 1 \}
  • Box 2 - {2,3,5,7} \{ 2, 3, 5, 7 \}
  • Box 3 - {4,6,9,10} \{ 4, 6, 9 , 10\}
  • Box 4 - {8} \{ 8 \}
×

Problem Loading...

Note Loading...

Set Loading...