### Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

### Negative Dice

Weekly Problem 16 - 2012
If the odd numbers on two dice are made negative, which of the totals cannot be achieved?

### Sum One Special

Weekly Problem 1 - 2007
Three integers have a sum of 1 and a product of 36 - what are they?

# Minus One Party

##### Stage: 3 Short Challenge Level:
\begin{align}
(-1) + (-1)^2 &= -1 + 1 = 0\\
(-1)-(-1)^2 &= (-1) - 1 = -2
\end{align}
Therefore:
\begin{align}
[(-1) + (-1)^2 ]\div [(-1)-(-1)^2] = 0 \div (-2) = 0
\end{align}

This problem is taken from the UKMT Mathematical Challenges.

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