Solution

35589

First name
Emma Dinnage
School
Wallington High School for Girls
Country
Age
13

For levels 1 and 2, find the difference between the numbers and then take the difference away from the first number to find the shift. If the result is positive, the numbers have been shifted up. If the result is negative, the numbers have been shifted down. For example: 14, 23, 32, 41, 50. The difference is 9 so that is the table. Subtract 9 from 14 and you get 5, so the numbers were shifted up by 5.

For levels 3 and 4, as these can be any numbers from the table, I put them in ascending order first. Then, as before, I found the differences, but again as these can be any numbers from the table, I found the Highest Common Factor (HCF - the largest number that all the other numbers are divisible by) and this gives you the table. To find the shift in these levels, you have to find the closest multiple of the table to the smallest of your set of 5 numbers. When you have found this, find the difference between the multiple and the number from your set. If you had to add, the shift is up and if you had to subtract, the shift is down. For example: 93, 324, 390, 489, 522 (I put these in order). The differences here are 231, 66, 99, 33 and these are all multiples of 33, so the times table is 33. The closest multiple of 33 to 93 is 99, and 93 is 99-6, so the numbers were shifted down 6.