Question

Brian is playing billiards with his friends at a sports club. The balls are arranged in a triangular frame, as shown in the given image.
Brian notices that there are 12 balls, numbered from 1 to 12 without repetition.

Find the missing numbers on the balls, if the sum of the numbers on the balls is 36 on each side of the triangle.

• A. A = 11; B = 9; C = 4
• B. A = 9; B = 4; C = 11
• C. A = 11; B = 9; C = 6
• D. A = 9; B = 11; C = 4

Answer 1

The correct option is D A = 9; B = 11; C = 4


We know that the sum of the numbers on the balls on each side of the triangular frame is 36.
Thus,
PQ = QR = RP = 36

Sum of the sides:
PQ = 12 + A + 5 + 2 + 8
36 = 27 + A
36 – 27 = A
9 = A

QR = 8 + B + 6 + 1 + 10
36 = 25 + B
36 – 25 =B
11 = B

RP = 10 + C + 3 + 7 + 12
36 = 32 + C
36 – 32 = C
4 = C

Thus, the missing numbers are:
A = 9; B = 11; C = 4