Lizzie came up with a divisibility test for a certain number :
Break a positive integer into two-digit chunks, starting from the ones place.
Find the alternating sum of these two-digit numbers, by adding the first number, subtracting the second, adding the third, and so on.
Find and show that this is indeed a divisibility test for m.
This is a divisibility rule for 11. Here's more information about divisibility rules: