Problem Teachers' Notes Hint Solution

# Magic Vs

Place each of the numbers $1$ to $5$ in the V shape below so that the two arms of the V have the same total.
How many different possibilities are there?
What do you notice about all the solutions you find?
Can you explain what you see?
Can you convince someone that you have all the solutions?
What happens if we use the numbers from $2$ to $6$? From $12$ to $16$? From $37$ to $41$? From $103$ to $107$?
What can you discover about a V that has arms of length $4$ using the numbers $1-7$?
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