Paul’s Puzzle Page - Contest #2
As this is being typed, the response to the first contest has been underwhelming. Perhaps we will have a last minute flurry of entries. I will be revealing the the correct (?) combination of answers on Thursday, September 13th. Again, you do not have to get it completely correct to win!
Okay, now for the second one.
As I promised (threatened), this is going to be a pure MATH problem. I love this puzzle and used it for about 25 years in all of the math classes I taught - regardless of level. It only requires a background of perhaps Algebra I and a little critical thinking to solve it completely. BUT, a local chapter of Mensa couldn’t come up with all of them until…
TRUE STORY: Sometime back in 1976, I was bending an elbow with a friend at the ol’ Deer Park Tavern. He was/is a member of the local chapter of Mensa and told me that no one in the group had been able to come up with two of the twenty answers to the puzzle below. Naturally, I wanted him to give me the problem. I pondered on it for a while and with the help of a pint of Guiness, came up with both of them. After giving him the answers scrawled on a damp napkin, he immediately called another member to tell him that the answers had been found. And, as they say, the rest is history.
Here’s you goal: come up with a mathematical expression using exactly 4 twos, no more - no less, that equals ONE. Also, come up with another expression using exactly 4 twos that equals the number TWO. Get the idea? You are to try to come up with an expression that works for every answer from one to twenty. To qualify for the prize, though, you only have to come up with 15 expressions, each with a different answer from one to twenty. Different expressions yielding the same result do not count.
I used this puzzle in every class because it utilizes the basic rule for ALL of mathematics - order of operations. Remember “Please Excuse My Dear Aunt Sally”? Regardless of high up you go in math, the same basic rule applies. So be sure that you pay strict attention to it. For example: 2+2/2-2 = 1, but (2+2)/2-2 = 0
Rules:
1) You must write legibly and be sure that all grouping symbols are clear. Write the numbers 1 - 20 in a vertical column down the left side of a sheet of paper (lined would be preferred). Fill in those that you come up with.
2) Your expressions must yield the exact number. No use of the “step functions”, that is either the one that automatically rounds up to the next integer or truncates any fraction and lowers to next integer. (To illustrate how these work, think of how the phone company might charge you two minutes for a one minute 13 second call - rounding up. Then there’s the practice of listing a bowling average at only 178, even if it is 178.95 - truncating)
3) You may NOT place a pair of twos next to each other to create a “22″. All twos are to be separated by some sort of mathematical operation and/or grouping symbol.
4) Again, some numbers have many expressions using 4 twos that work. List only one. You will not get “extra credit”, although I might post particularly clever ones on this blog after all entries are submitted.
5) You’re not going to like this one - Only one entry per person and if ANY of your expressions do not yield the number you claim, your entire entry is disqualified!! So be careful. One year, a student asked a professor at the U of D for help. He was quite upset when I diagreed with his attempt, then humbled when it was pointed out that a set of parenthesis was misplaced in his solution. I have shown the entire solution to perhaps 3,000 people over the years. Find one!!
6) Everyone who manages to get at least 15 correct will be put into the drawing for the $25 worth of 3/4″ green-tagged items in the shop. As a bonus and incentive to keep trying, for each one beyond 15 that you get, your potential prize goes up $5. Yep, get all 20 and you could win $50 worth of stuff if your name is pulled!
7) Entries must be submitted by 5:00 PM on Sunday, September 23rd. Good Luck!
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