William asked in Science & MathematicsMathematics · 8 months ago

# Mind Tickler to solve?

Three regular dice are stacked one upon the other. The dots on each pair of touching sides add up to 5 and the face on the top of the stack shows an odd number of dots. Given that the dots on each pair of opposite faces on each die add up to 7, how many dots are on the face at the bottom of the stack?

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• 8 months ago

The numbers (of dots) on the top and bottom (we'll sort which shortly) of the middle die are 3 and 4, so the numbers of dots facing them are 2 and 1 respectively.

"the face on the top of the stack shows an odd number of dots" so the number of dots on the bottom of the top die is even, so two, making the top number on the bottom die a 1, and so there are 6 dots are on the face at the bottom of the stack.

• 8 months ago

The sum of the opposite faces add up to 7, so with 3 dice, all the numbers add up to 21.

We know that four of the numbers (the inside faces) add up to 10 (two times 5). That leaves the top and bottom to add up to 11.

If the top number is odd, it has to be 1, 3 or 5. It only works if the top face is 5 and the bottom face is 6.

Summary:

[5] <-- top face

[2] \__ sum = 5

[3] /

[4] \__ sum = 5

[1] /

[6] <-- bottom face