# Sunday Times Teaser 3071 – Three-Cornered Problem

*by Oliver Tailby*

#### Published Sunday August 01 2021 (link)

I have a set of equal-sized equilateral triangles, white on one face and black on the back. On the white side of each triangle I have written a number in each corner. Overall the numbers run from 1 to my age (which is less than thirty). If you picture any such triangle then it occurs exactly once in my set (for example, there is just one triangle containing the numbers 1, 1 and 2; but there are two triangles containing the numbers 1, 2 and 3).

The number of triangles that contain at least one even number is even.

The number of triangles that contain at least one odd number is odd.

The number of triangles that contain at least one multiple of four is a multiple of four.

How old am I?

Based on data analysis.

@Frits:

I can see your code gets the same answer as Brian’s code, but am not sure how your code works in relation to the requirements of the puzzle description?

How does data analysis relate to this puzzle?

Perhaps I am missing something.

@GeoffR, There only is an indirect relation with the requirements of the puzzle.

I wrote down all possible triangles for ages 2 – 5 and verified Bryan’s list of evens, odds and mlt4s numbers.

I was curious to know if there was a pattern in these numbers.

So the data analysis was on the list of evens, odds and mlt4s numbers.

I can’t explain these formulae.

What is there in the teaser statement that excludes the triangle (1, 1, 1)?

Including this triangle results in a non unique solution.

Hi John,

There is nothing mathematical that eliminates the solution with the age equal to one. But Oliver Tailby could not have been one when he wrote the teaser so I assume that he expects us to eliminate this solution.

Sorry Brian, I didn’t see your comment on line 17.

“there are two triangles containing the numbers 1, 2 and 3”.

So the age must be at least 3.

@Jim,

Is that a comment on Frits’ solution or on my own (or both)? I start at 2 in order to count the (1, 1, 2) triangle. I pre-counted the (1, 1, 1) triangle only to avoid outputting the age = 1 solution.

It was in response to the comments about eliminating the age = 1 solution.