Problem 10 · 2011 Math Kangaroo
Medium
Logic & Word Problems
casework
The picture shows three dice stacked on top of each other. The sum of the points on opposite sides of a die is 7, as usual. The sum of the points on the faces that touch each other is always 5. How many points are on the face marked X?
Show answer
Answer: E — 6
Show hints
Hint 1 of 3
Opposite faces of one die sum to 7, and the two faces where neighbouring dice touch sum to 5.
Still stuck? Show hint 2 →
Hint 2 of 3
Start from the visible front dot on the bottom die and step up the stack one face at a time.
Still stuck? Show hint 3 →
Hint 3 of 3
Use the two rules to relate each touching face to the one above it until you reach X.
Show solution
Approach: step the two face-sum rules up the stack to the top face X
- Write the chain from the bottom die upward: opposite faces of a die sum to 7, and each pair of touching faces between two dice sums to 5.
- Starting from the orientation fixed by the visible front 1, each touching pair forces the next face, and these alternating 7s and 5s carry the value up the column.
- Following the chain to the very top face leaves X = 6, the only value keeping every die face between 1 and 6.
- So X shows 6 points, choice (E).
Mark:
· log in to save