You can see three sides of each of two dice, and notice that the total number of pips showing is a perfect cube.
What are the numbers of pips on each face that you see?
(In reply to
Problem Solution by K Sengupta)
The minimum sum of the six visible faces in two dice = 2*(1+2+3)=12
The maximum sum of the six visible faces in two dice = 2*(4+5+6)=30
Since the sum of the cubes of the 6 pips is a perfect cube, it must equal 27, being the only perfect cube between 12 and 30.
Now we know that if #pips in two faces of a die sum to 7, then one of the faces is visible and he other is out of sight.
Accordingly, the valid faces and the sum of the #pips in the 3 faces are furnished hereunder as follows:
Visible Faces of a die Pip Sum
1,2,3 6
1,2,4 7
1,2,6 9
1,3,5 9
2,3,6 11
2,4,6 12
3,5,6 14
4,5,6 15
Referring to the above table, we observe that the only way the number of pips in 6 faces in the two dice sum to 27 is by having the sum of 12 pips in one face and the sum of 15 pips in the other.
This is achievable when the three faces in one die are:(2,4,6) and (4,5,6) in the other.
Edited on March 19, 2022, 2:01 am
Explanation for Problem Solution
