Negative dice
If the odd numbers on two dice are made negative, which of the totals cannot be achieved?
Age
11 to 14
Challenge level
Problem
I have some strange dice: the faces show the numbers 1 to 6 as usual, except that the odd numbers are negative (i.e. -1, -3, -5 in place of 1, 3, 5).
If I throw two such dice, which of the following totals cannot be achieved?
a) 3
b) 7
c) 8
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Student Solutions
Answer: you cannot make 7 (option b).
3 = -1 + 4 or -3 + 6
8 = 4 + 4 or 2 + 6