**Source:**IBM Ponder This Dec 12 ( http://domino.research.ibm.com/comm/wwwr_ponder.nsf/challenges/December2012.html ) - Mailed to me by Aashay Harlalka (Final Year Student, CSE, IITB)

**Problem:**

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.

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

1 2 1

4 3 4

2 1 2

Update (24 June 2014):

**Solution:**Available on IBM Research Ponder This - December 2012 Solution