# Discussion of Question with ID = 009 under Cubes-and-Dice

## This is the discussion forum for this question. If you find any mistakes in the solution, or if you have a better solution, then this is the right place to discuss. A healthy discussion helps all of us, so you are requested to be polite and soft, even if you disagree with the views of others. The question and its current solution has also been given on this page.

### Question

Six different dice with their top faces erased have been given. The opposite faces of each dice have numbers which add to 13. All dice have the numbers from amongst 4, 5, 6, 7, 8 and 9 printed on them.

If the odd-numbered dice have even numbers at their bottom faces, what is the sum of those even numbers ?

A
24
B
22
C
20
D
18
Soln.
Ans: b c

The odd numbered dice are 1st, 3rd and 5th. Consider this deduction.

1. Dice No. A: Face opposite 6 is 7 because 6 + 7 = 13. Similarly, face opposite 4 is 9. So, the numbers that appear on the sides are 4, 6, 7 and 9. Out of the remaining 5 and 8, the bottom face is 8.
2. Dice C: Similarly, 8 is at the bottom.
3. Dice E: 4 is at the bottom.

So sum is 8 + 8 + 4 = 20.

p> The odd numbered dice are A, C and E. Consider this deduction.

1. Dice No. A: Face opposite 6 is 7 because 6 + 7 = 13. Similarly, face opposite 4 is 9. So, the numbers that appear on the sides are 4, 6, 7 and 9. Out of the remaining 5 and 10, the bottom face is 10.
2. Dice C: Similarly, 8 is at the bottom.
3. Dice E: 4 is at the bottom.

So sum is 10 + 8 + 4 = 22.

### Comments and Discussion

NOTE: 30-Dec-2016, Corrections done as suggested by Charan KR.