a. Choose a two-digit number such that the number in the tens place is 1 greater than the number in the units place. Reverse the digits in your number, and subtract this number from your original number; for example, 87 — 78 = 9. Make a conjecture concerning the result of performing this operation.
b. Choose any two-digit number such that the number in the tens place is 2 greater than the number in the units place. Reverse the digits in your number, and subtract this number from your original number; for example, 31 - 13 = 18. Make a conjecture concerning the result of performing this operation.
c. Prove that for any two-digit number, if the digits are reversed and the numbers subtracted, the difference is a multiple of 9.
d. Investigate what happens whenever two-digit numbers with equal digit sums are subtracted; for example, 62 - 35 = 27.
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