The Solution - Art and Science : George McBean/Detlef Palm

You may have exercised your brain with last week's Cannonball Puzzle. I received several responses by email, most of them correct. To find the answer to this puzzle or to any other problems of daily life, one does not need to be entitled to a corner office in the UNICEF office on 44th Street. And it doesn't matter whether you are a scientist, artist, intellectual, or elder stateswoman. 

George McBean was the first to provide the correct solution: George sent in two images that tell it all:

The next solution is from a colleague, who wishes to remain unnamed. Using some formula found by the 9-year old Carl Friedrich Gauß 250 years ago, the colleague submitted that the number of cannonballs in a pyramid with n cannonballs at the length of one side is:

Number of balls = n*(n+1)*(n+2)/6 

For those who prefer a computer doing the thinking, the following solution was sent in by a colleague who is a computer programmer:

<code>
#!/usr/bin/awk -f
BEGIN {
n = 6;
for (i = 2; i <= (n + 1); i++) {
  kt = kt + (i - 1);
  k = k + kt;
}
print k;
}
</code>

Whatever method you favour: If the number of balls on one side is 6, the number of cannonballs on the pile will be 56.

If the number of balls on one side is 17, the number of cannonballs will be 969.

If the number of balls on one side is 31, the number of cannonballs on the pile will be 5456, which are a lot of cannonballs, but represent only half the number of nuclear warheads currently in use globally.