Regifting Robin

[Bees Knees]

http://www.regiftable.com/regiftingrobinpopup.html

She gets it right every time, assuming you do the math correct and actually think about the answer.

Anyone care to explain why?

[JohnH]

Yes. This exercise is dependent upon a characteristic of the "Base 10" numbering system. When subtracting the sum of the two digits from the original number, the result will always be the number "9" or a multiple of "9".

Looking closely at the list of gifts, you will see that the gift listed as 9, 18, 27, 36, 45, 54, 63, 72, 81 etc will always be the same item for any given list. Since the result you got when you did the original math will always be 9, 18, 27, 36, 45, 54, 63, 72, 81 etc., the name of the gift will always be correct. I like how they mix up the list and result each time you go through the exercise - makes it more interesting.

(Notice that the sum of the two digits in the result is also equal to "9" when they are added together. I like this exercise because it indirectly ties into my current signature as well.)

[OtisMozzetti]

Yes. This exercise is dependent upon a characteristic of the "Base 10" numbering system. When subtracting the sum of the two digits from the original number, the result will always be the number "9" or a multiple of "9".

The original number can be represented as 10m + n, where m and n are nonnegative integers. The "two digits" are m and n. The requested calculation above is 10m + n - (m +n) = 9 m, where m is known to be an integer. Thus the result is a multiple of 9.