Math "puzzles" for 12 year olds

[shogunhb]

Generally, when I'm busy, I'll let the calls go to voicemail and call back later. But several calls in a row usually means important, so I answered. My mom called me several times last night during game, so I ducked out to find out what was wrong

Comments

[bronzite]

If I had to do that without a computer, I'd start with a "best guess" solution (it doesn't matter how good it is), and switch numbers from high-value positions (multiplicative and additive) to low-value positions (subtractive and divisive) or vice versa depending on whether or not my current solution was coming out high or low. I'm not sure how long that would take, but "walking it in" is the only means I can think of.

[shogunhb]

I tried that for an hour and couldn't nail it down. You could get lucky.

[teddywolf]

You want I should ask my cousin who teaches university maths?

[shogunhb]

Sure. I think that the "proper" way to solve it mathematically would use Matrix Calculus. Of course, I've forgotten all my Matrices and I doubt any of the kids in my niece's class know it.

[teddywolf]

I have not sent it to my cousin yet. Now this said, I do have a couple of bits that are important

[ultimatepsi]

This is the strategy I would use as well, except that because the fractions are both equivalent to a*b/c you get a lot of possibilities, including 3*6/9.

It's an ugly problem, and I wouldn't give it to my students.

[usernamenumber]

If you don't mind unflocking this, I have some friends whose opinions might be very interesting (CTY math instructors). If that's not feasible for some reason, mind if cut/paste the post into an email to them?

[neuromancerzss]

Well, if they type it into Google in the same way you posted it there's a solution page (listing answers, but not method), so maybe this is a cheat-trap?

My gut instinct is to reduce it to just 6 numbers. Two numbers go into the divisions and create whole numbers and the 1 is placed in the second set of multiplicative operations, so then you only have 6 numbers to fit into the form "a*b+c*d+e*f=100". It's still not an easy problem.

[rosinavs]

By "order of operations", do you mean the standard algebraic order of operations (which is usually taught after age 12) or the order in which they appear from left to right (what is usually used before kids learn PEMDAS)? In any case, this problem is not age-appropriate. It sounds to me like the teacher is trying to teach them at a higher level in general than what is appropriate.

If PEMDAS is the order of operations, then the earlier suggestion of three numbers added together to make 100 is good, you then need to figure out the multiplications and divisions to make them work.

If left to right is the order of operations, the last number must be a factor of 100, which means it must be 1, 2, 4, or 5.

[shogunhb]

PEMDAS

[rosinavs]

When I have more time to think about it I will. If you want all whole number partial answers, that limits the numbers you divide by to 1, 2, 3, 4, and 6.

[shogunhb]

Or 8 (but only for the first section). You get a fraction momentarily, but the section is a whole number.

4/8*6 or 6/8*4

Yes, you can reduce the number of guesses to a more limited set of "good" guesses, but you're still looking at thousands of possibilities. I'd like to see how long it takes a math PhD to get an answer without a computer or to give up.