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### 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.

- 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.
- Dice C: Similarly, 8 is at the bottom.
- Dice E: 4 is at the bottom.

So sum is 8 + 8 + 4 = 20.

- 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.
- Dice C: Similarly, 8 is at the bottom.
- 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.