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?

Question

Rhett Knox

Mathematics

6 August, 12:46

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?

+5

Answers (1)

Know the Answer?

Tori Hubbard · Answer 1

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