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Negative Dice

Stage: 3 Short Challenge Level: Challenge Level:1
See all short problems arranged by curriculum topic in the short problems collection

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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If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

This problem is taken from the UKMT Mathematical Challenges.