# Pattern Problem (3 x 3 grid)

My student showed me this problem. I can't seem to make heads or tails of it.

I've tried trying to spot the pattern horizontally or vertically, but there's either too many things happening (different numbers of triangles and the position).

Hopefully, you can give me some insight to the problem. These triangles

'Sum' both horizontally and vertically with triangles in the same position

The rules:

- An empty space plus a triangle = the triangle
- △ + ▽ = nothing
- Similar triangles create a triangle facing the other way (▽ + ▽ = △)

As @Bass points out this can be represented by addition. If a gap = 0, △ = 1 and ▽ = 2 then

We can add two together and find the result by using mod 3.

0 + 0 = 0
0 + 1 = 1
0 + 2 = 2
1 + 1 = 2
1 + 2 = 0 (mod 3)
2 + 2 = 1 (mod 3)

So using this we can find any result given two inputs.

So therefore the correct answer is

C

Hopefully that makes sense!

• I see what you're saying. The pattern "fits". Thanks! – chuckong083608 Jul 15 at 16:05
• @chuckong083608 glad I could help and glad you can understand! It was a bit tricky to try and explain :) – Beastly Gerbil Jul 15 at 16:06
• If you choose 1 for △ and 2 for ▽ (or vice versa), you can just do regular addition modulo 3. (If the sum is 3 or more, subtract 3.) – Bass Jul 15 at 16:37
• @Bass that is true! I'll add that in thanks :) – Beastly Gerbil Jul 15 at 16:38