Perceptual Puzzle #49- Balanced Triangle -
Can you put the numbers 1 through 9 in the nine circles below so that each side of the triangle adds
up to 17? Note: You can't use a number more than once.
HINT: This is easier than it looks. Use logic to figure out which numbers must go
in the corners.
ANSWER:
The first step is to determine the value in the three vertices (points)
of the triangle. Label the circles of three vertices a, b, and
c and the rest d through i, the order of these
is unimportant. So we know
1) a + d + e + b = 17
2) b + f + g + c = 17
3) c + h + i + a = 17
4) a + b + c + d + e
+ f + g + h + i = 45 (since the sum
of the numbers from 1 to 9 adds up to 45).
There are probably other ways to manipulate the equations to solve, but here is one way. Adding equations
1, 2, and 3 gives:
5) 2a + 2b + 2c + d + e
+ f + g + h + i = 51.
Subtracting 4 from 5 gives: a + b + c = 6 which means
the values are 1, 2, and 3. So put the number 1, 2, and 3 in the vertices. The middle numbers on each side
have to add up to 12, 13, and 14 respectively (depending on the two surrounding vertices). The value of
the remaining circles should be easy to find.
See the image below:
Do you have a
suggestion for this puzzle (e.g. something that should
be mentioned/clarified in the question or solution, bug, typo, etc.)?
