IBM Ponder This #176 · December 2012

36 people live in a 6x6 grid, and each one of them lives in a separate square of the grid. Each resident's neighbors are those who live in the squares that have a common edge with that resident's square.

Each resident of the grid is assigned a natural number N, such that if a person receives some N>1, then he or she must also have neighbors that have been assigned all of the numbers 1,2,...,N-1.

Find a configuration of the 36 neighbors where the sum of their numbers is at least 90.

Finding a sum of 90+N will earn you N stars near your name.

As an example, the highest sum we can get in a 3x3 grid is 20:
1 2 1
4 3 4
2 1 2

An accompanying riddle, relating to a generalized version of this problem, appears in this month's Using your Head is Permitted
( http://www.brand.site.co.il/riddles/201212q.html).

Solution

Best opened after a real attempt

To be added.