## Tricky and Unusual Math ProblemsApril 26, 2012 As if mathematics wasn't difficult enough, students are faced with tricky exam questions. Students of my generation preferred multiple choice questions over other types. Our multiple choice questions were posed as follows:Which of one of the following is a prime number?
a) 4Students of my children's generation faced the reinvented version of the multiple choice question of the type, Mary has three coins in her purse.[1] These coins can have a combined value of
a) 3, 7 or 12, but not 14Problems like this are a sneaky way of putting three problems into the space allotted for one. There are many jokes that are posed as unanswerable questions, such as, "A man walked into a restaurant. What color socks was he wearing?" There's actually a math problem that sounds just as unanswerable, but it does have an answer. This problem is called, variously, "The Census-Taker Problem" and "The Ages of Three Children Problem." I was reminded of this problem by a recent posting on arXiv by I.J.L. Garces and Mark L. Loyola of the Department of Mathematics of the Ateneo de Manila University.[2] Here's their version of the problem. A census taker knocks on a door. A mother answers.As if this isn't confusing enough, what's that question about dogs? The simple answer is that there are just two sets of three numbers that satisfy the condition that the product is 36; namely, {9,2,2} and {6,6,1}. The question about the dog is to determine if there is an older daughter, resulting in the {9,2,2} combination. There is a chance that the mother might have said that none of her children like dogs, so another question would be needed; but then the problem wouldn't be so memorable. Another paper, posted by Tanya Khovanova on arXiv, presents many tricky arithmetic problems.[3] Khovanova writes an interesting blog[4] and she has a web site, also.[5] Here are a few of these tricky arithmetic problems.[3]
## References:- US coins have the following cent values: 1, 5, 10. 25, 50, 100.
- I.J.L. Garces and M.L. Loyola, "Revisiting a Number-Theoretic Puzzle: The Census-Taker Problem," arXiv Preprint Server, April 10, 2012.
- Tanya Khovanova, "Tricky Arithmetic," arXiv Preprint Server, April 13, 2012.
- Tanya Khovanova's Math Blog.
- Tanya Khovanova Web Site.
Linked Keywords: Mathematics; student; exam; baby boomer; multiple choice; prime number; Generation Y; joke; The Census-Taker Problem; The Ages of Three Children Problem; arXiv; Department of Mathematics; Ateneo de Manila University; dog; set; product; Tanya Khovanova; arithmetic; Gathering for Gardner; Martin Gardner; Scientific American; Konrad Jacobs; Wikimedia Commons. |
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