fanguiano10
Answered

Level B
Pick any 2‐digit number where not all the digits are equal. Order the digits
from highest to lowest to create the largest number. Next order the digits
from lowest to highest to create the smallest number. Find the positive
difference between the two numbers. Investigate different solutions you find.
Are there patterns? If so, what patterns did you find?



Answer :

DavidOrrell
The number has 2 digits - let's call them x and y. The positive difference between the two combinations (lowest-highest and highest-lowest) is always equal to the positive difference of x and y, multiplied by 9.

For example:

76 and 67: 76 - 67 = 9 and ((7-6)*9) = 1*9 = 9
73 and 37: 73 - 37 = 36 and ((7-3)*9) = 4*9 = 36

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