# Filling an array

• Aug 24th 2013, 07:33 PM
Wilmer
Filling an array
There are N numbers available: from 1 to N.

The rows of a 8 by C array are each filled with C numbers,
each row ending up with C different numbers.

A number may appear a maximum of 4 times,
in other words, in a maximum of 4 rows.

Every 2-row-combo has a minimum of 2 numbers in common.

What is minimum N?

Solution is minimum N = 12; this is the resulting array (C = 6):
1: 01 02 05 06 07 08
2: 01 02 05 06 07 08
3: 01 02 09 10 11 12
4: 01 02 09 10 11 12
5: 03 04 05 06 09 10
6: 03 04 05 06 09 10
7: 03 04 07 08 11 12
8: 03 04 07 08 11 12

OK. Changing the conditions a bit (or making it tougher!):

There are N numbers available: from 1 to N.

The rows of a 20 by C array are each filled with C numbers,
each row ending up with C different numbers.

A number may appear a maximum of 10 times,
in other words, in a maximum of 10 rows.

Every 5-row-combo has a minimum of 2 numbers in common.

What is minimum N?
• Aug 27th 2013, 02:45 AM