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Here is how Harry tackled the problems at Level 4...

This time I have numbers 123, 59, 171, 219 and 91
1) Put the numbers in order and find the differences
59 (+32) 91 (+32) 123 (+48) 171 (+48) 219
2) Find the highest number that goes into all the differences
Factors of 32 = 1, 2, 4, 8, 12, 16 and 32
Factors of 48 = 1,2,3,4,6,8,12,16,24 and 48
So 16 in this case. This gives you the times table that has been shifted
3) Write out the 16x table, which will help you find the shift
In this case it is either 16 minus 5 or 16 plus 11. You can check it works for each number you were given
4) There will always be two answers because you can either add, or minus from the number you were given to get to a number in the 16 x table