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The problem is explained below, but you may wish to scroll to the foot of the page to watch a video of the NRICH team presenting this challenge.
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?
How do you know you've got them all?
What do you notice about all the solutions you find?
Can you explain what you notice?
Can you convince someone that you have all the solutions?
What happens if we use the numbers from 2 to 6?
Can you explain what you notice this time?
Here is a video of the NRICH team presenting the challenge. You could just watch the start to check that you understand the problem, or you may like to pause the video and work on the task at various points.
If you have enjoyed this problem, you might like to explore Magic Letters.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.