Triangle Puzzles Notes on Investigation

1) If we have 10 stones then all the puzzles will have numbers at the

end of the arrows that sum to 20, with none of the numbers being greater than 10.

With 8 stones the numbers must total 16 with no number being greater than 8. Possible

Puzzles are;

8,8,0 8,7,1 8,6,2 8,5,3 8,4,4

7,7,2 7,6,3 7,5,4 6,5,5

2) As with the Sum Puzzles we can use logic or algebra.

Logic

There must be 8 pebbles in the bottom circles so there must be (10-8) =2 in the top circle.

If there are 2 in the top then there must be (3- 2) = 1 in the left circle.

If there are 2 in the top circle then there must be (9-2) = 7 in the right circle.

Using Symbols

Let the number of stones in the circles be a,b and c.

Then make as many equations as you can

a + b + c = 10

a + b = 3

b + c = 9

c + a = 8

and solve by substitution