# Numbers in Triangle Rows of 3 are equal rows of 4 are equal

1. Oct 14, 2008

### Dragon_Wizard

Ok I'm new here and I don't know how to find answers to puzzles.

I've got a few and my brain isn't working.

Picture a triangle with circles in it. Place the numbers 1-10 in the circles on the triangle so that the sum of Rows of 3 are equal and the sum of rows of 4 are equal

O
O O
O O O
O O O O

(If the picture of the triangle doesn't come out it 1 circle on top, then 2, then 3 then 4. The perimeter has 4 circles on all three sides.

2. Oct 15, 2008

### DyslexicHobo

Just to help with the picture, try to code tag

Code (Text):

o
o  o
o  o  o
o  o  o  o

3. Oct 16, 2008

### davee123

I believe there are 12 solutions to this, which are variants on 2 different patterns. You can rotate by 120 degrees and get a "new" solution effectively, or flip it along one of the 3 axes of symmetry-- giving you 6 variants on a single solution, and 12 patterns all together, since there are 2 "core" solutions.

Two of the variants on the core solutions are:
2
7 8
3 4 10
9 5 6 1

2
8 6
4 7 5
9 3 1 10

DaveE