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## Mensa Matters

These two mathematics-related questions are from a sample Mensa Exam, posted on their newsgroup rec.org.mensa in the early 1990s:

[1] Sally likes 225 but not 224; she likes 900 but not 800; she likes 144 but not 145. Does she like 1600 or 1700?

[2] Put the appropriate plus or minus signs between the numbers, in the correct places, so that the sum total will equal 1.

0 1 2 3 4 5 6 7 8 9 = 1

Source: The Internet Yellow Pages, 1995, p. 518

Hint: For question [1], list the numbers in two columns...like and dislike. Look for a common trait.

For question [2], look at it as sub-problems. For example, if you could insert signs so that (2 3 4 5 6 7 8 9 = 0), you are done, etc. Also, do you think it is legal to do something such as 0+12-3...?

Solution Commentary: On question [2], if you got a solution, is it unique? That is, can you either find another solution or prove that yours is the only possible solution?