Zardoz wrote:

Don't add the numbers up. Instead, consider the primal clue:

Only the way a man is when he is

hidden is how he is. A shallow

glimpse can deceive. Look deep, ponder

and recognize all that is hidden

Now, which numbers are "hidden" for each color?

Dr. Worm wrote:

[..]

The way I see that you find the solution is:

1. Add up the three numbers for each pillar. You get:

1st pillar: 9

2nd pillar: 6

3rd pillar: 9

4th pillar: 8

2. Subtract the numbers you get from 10.

That gives you the solution: 1, 4, 1, 2.

My question is, how are you supposed to know to subtract from ten? [..]

Interesting.

I would like to say, Dr. Worm, you were not absolutely wrong with adding the numbers up.

Consider that the "possible" numbers were supposed to be 1, 2, 3 or 4 here. Now, the sum 1+2+3+4 is ... 10.

And this will work with ANY set of numbers, starting with 1, up to any number "n":

If you are looking for a single missing number y in a set [1, 2, ... , y-1, y+1, ... n-1, n] you can just add up all numbers in the given set, substract it from the sum of numbers [1..n] and you will get the missing number.

Sidenote: It may seem useless to make such additions and subtractions because in this example you can easily *see* which number is missing, but assume a set of more (unsorted) numbers but one missing - e.g. a set of billiard balls. With this trick you can determine the missing ball without the need to sort the list.

For example, if you get a sum of 112 with 14 balls, then ball 8 is missing to make the set of 15 balls complete (sum 120).

shorah