7. On a standard dice, the sum of the numbers of pips on opposite faces is always 7. Four standard dice are glued together as shown. What is the minimum number of pips that could lie on the whole surface?
A 52
B 54
C 56
D 58
E 60
Solution
D

Since the sum of the numbers of the pips on opposite faces is 7 , the sum of the numbers of pips on the top and bottom faces of each dice is 7 as is the sum of the numbers of pips on the front and the back faces of each dice. To obtain the minimum number of pips on the surface, the dice should be arranged so that there is a 1 showing on both the left- and right-hand ends of the shape. Therefore the minimum number of pips that could lie on the whole surface is $4 \times 7+4 \times 7+1+1=58$