Problem 14 · 2021 Math Kangaroo
Medium
Algebra & Patterns
sum-constraint
The diagram shows 3 hexagons with numbers at their vertices, but some numbers are invisible. The sum of the 6 numbers around each hexagon is 30. What is the number on the vertex marked with a question mark?
Show answer
Answer: B — 4
Show hints
Hint 1 of 2
Each hexagon's six vertex numbers add to 30; shared vertices link the hexagons.
Still stuck? Show hint 2 →
Hint 2 of 2
Set the unknown shared values from one hexagon's total, then use them in the hexagon with the '?'.
Show solution
Approach: use the constant hexagon sum and shared vertices
- Every hexagon totals 30, and two neighbouring hexagons share the two vertices on their common edge.
- Comparing the middle hexagon (holding the ?) with a neighbouring hexagon, the shared vertices appear in both totals and cancel, so the difference of their other vertices is forced.
- Filling the blanks from the visible numbers that way pins the marked vertex to 4.
Mark:
· log in to save