The numbers are written on a blackboard.
On each turn, Anna picks two numbers, and Bob erases these two numbers, and then adds their product, sum or positive difference to a separate total.
For example, If Anna picks 2 and 3, Bob erases them and so the separate total is .If Anna picks 1 and -1 next, Bob erases them, takes the positive difference ( ) and adds it to the total ( ).
Eventually, there will be no numbers left on the board. Bob is trying to maximise the total and Anna is trying to minimise it.
If Anna and Bob both play optimally, what will the total be?
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