Question

Six dice with their top faces erased have been given. The opposite faces of the dice have dots which add up to thirteen. Work out the number of dots on the top faces and answer the given question.

If dices II, IV and VI have odd number of dots at their top faces, what would be the total number of dots?

• A. $21$
• B. $20$
• C. $19$
• D. $18$

Answer 1

The correct option is A $21$

The numbers on dice are $4,5,6,7,8,9$
It is given that sum of opposite faces is $13$.
So, no. of dots on the opposite pair of faces can be $\left(49\right),\left(58\right),\left(67\right)$
We need to find odd numbers of possible dots for
Dice II- We have $8$ and $9$, then numbers on top face of dice can be $6$ or $7$.
Since $7$ is odd, so top face has $7$.
Dice IV - We have $4,5$ then number of dots on top face can be $6$ or $7$.
Since $7$ is odd, so top face has $7$ no. of dots.
Dice VI- We have $4,8$ then number of dots on top face of dice can be $6$ or $7$.
Since $7$ is odd, so top face has $7$ no. of dots.

Thus, the total no. of dots on top face $=7+7+7=21$.

Hence, option A is correct.