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
filled star empty star empty star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

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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