OT, but I need math help


OK, this is off-topic, but I'm stumped and I need some brainy math people to help me find the pattern here. The question is, how is the last number derived from the first two in these four examples? This puzzle was designed to be solved by third graders, so no higher-order math should be required. I wrote the author of the textbook where I found this, but he has not responded yet. Here is the deal:

3 * 4 --> 5
4 * 7 --> 1
8 * 4 --> 0
1 * 2 --> 9
Any ideas, guys and gals?

Don Shepherd


+ CHS 12 +




An RPN solution. Very appropriate. 8)


But that will not work on the HP-35 unless we add an extra CHS. I should have posted the following, which works for all RPN HP calculators:


Sometimes we have trouble trying to solve certain problems, not because they are hard but because they are easy. Once I was given a problem and after an hour trying to solve it, to no avail, I quit. Two months later, when I opened the drawer where I had kept it, the solution popped up in front of me. I can understand Don's trouble with it.




When I wa sin 5th grade my math teacher gave us an example of two linear equations. I just looked at it, tried in my mind a could of numbers and gave him the solution. He was very impressed. He gave the same question to the other section, but no one solved it. It IS how you perceive the problem that allows the brain to analyze it and then solve it.


Thanks Gerson, Howard, and Namir. You are right on! I never noticed that each set of 3 numbers added up to 12. I was actually doing the multiplication and trying to relate the product to the number on the right, with no success.

I think this relates to the math skills that a third-grader has, and I imagine that includes addition and subtraction, but maybe not multiplication. I think it also involves clock arithmetic, where kids solve 3 + 4 by starting at 12 on the clock face and counting "clockwise" to get the answer. If a kid sees the symbol "*" or "X" and does not understand what it really means, that same kid might just start at 12 and go counter-clockwise, and arrive at the number on the right.

Gerson, I tip my hat to you!

Don Shepherd
Louisville, KY


Thanks, Don. Am I allowed in 4th-grade now? :-)

Relating this problem to a clock makes a lot of sense. But when I read it was a problem for third-graders, the first image that came to my mind was this:

I don't know why I thought of this, perhaps because at the time we solved problems like this: "You have three eggs and get four more. How many more do you need to make up a dozen eggs?". However, this was a problem presented to first or second-graders as far as I can remember (1st-grader in 1968).

Best Regards,

Gerson W. Barbosa

Curitiba, PR Brazil (25°25'47.9" S; 49°16'19.5" W)


It occurs to me that the third graders (if they aren't mythical) may well have been given such a lesson just before being asked to answer that question.


I was confused... LOL!... because I took the "*" to be multiply; for example, I entered 3, then 4, then ENTER then "x" then + then +/- (I was using a 32SII) then + and was totally mystified at first!

I guess one has to be a kid...


Yes, the asterisk is bound to confuse anyone who codes in a high level language. BASIC, C, C++ FORTRAN, Pascal, Modula, Java, Perl, Python and many others all use the "star" as the multiply operator. A third grader of yesteryear would have been blissfully ignorant of that usage, although I'm not sure about the more recent crops.

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