Look, I’m not saying the people who made the problem harder than it already was (by solving for other letters than O) are idiots, I’m just saying they took the wrong approach, and that shows how hard it is to find the optimal approach, which IMO is the only one that a fifth grader would understand. The average fifth grader doesn’t have the resources to follow most of the solutions offered.
If you are in Minneapolis and you want to go to St. Paul, you will eventually arrive there if you head due west long enough, but that’s not the correct way to do it, and there’s a good chance you will not have the resources to succeed.
Just because it’s hard for adults doesn’t mean it’s necessarily hard for fifth-graders. A lot depends on whether you’ve dealt with problems like this before. The book Pyper linked to above is full of this sort of thing.
Obviously O<5, R=0, 4 * any digit < 40
Next 4O <= 16 and even with carrying over from the 4N the result would be <= 19. Thus F=1.
Next 4E ends with 0 so E=5 since R already equals 0.
since 4N + 3 >= 10 we know that N is either 2, 3, or 4
So now we have ON5 + 1OU0 = 1IV5 and ON5 * 4 = 1OU0
Now it gets tricky. 4N+2 needs to end in U which means U = 0, 4 or 8. Since U =/= 0, that means that (N,U) = (3,4) or (4,8)
If N=3 then O35 * 4 = 1O40 thus 4O+1 = 10+O which yields O=3. But wait! N already equals 3.
If N=4 then O45 * 4 =1O80 thus 4*O+1 = 10+O and O=3. 345 * 4 = 1380. As a check: 345 + 1380 = 1725 giving I=7 and V=2.
Maybe I am underestimating myself, and I don’t know about you, Saint Cad, but when I was in fifth grade there is no way I could have gone through this process.
Hell, I went into this thinking “solve for O” meant “solve for zero” and was trying to come up with some operation that would end up as 5+4=0.
Recently there was a discussion of “new math” in another thread. My reaction to this problem is exactly what happens when you look at a new math problem with an old math mindset!
I think you may be underestimating yourself. I remember doing pretty complicated logic puzzles and math problems at that age. They took longer than they take now, but that’s sort of the appeal. At that age, for certain types, focus is not really a limitation and brute force methods aren’t seen as tedious as they become later.
And a problem like this one there aren’t really that many possibilities, especially once you see the first few “obvious” restrictions (the R=0 and E=5 ones). Then it’s just realizing that O < 5 and you can solve it by trial and error from there.
I distinctly remember the puzzle books of the kind Senegoid described - and that would have been 4th or 5th grade, I think.
I used to give problems like this to my seventh-graders, but as mentioned above, we worked samples in class and the problems themselves were extra credit. Some liked it and did well; others didn’t. It’s a problem in number sense, really, not algebra.
I remember seeing this exact problem at some point in my schooling. If I had to guess, it was in 6th or 7th grade. However, it doesn’t seem unreasonable to give to an advanced 5th grader, or as extra credit.
If you’re familiar with arithmetic and willing to guess and check, the answers fall out without too much trouble. I think most of the problems us grownups are having are due to trying to take too vigorous an approach.
But I don’t see a fifth grader being willing to guess and check. I sure wasn’t. I’d learned a long time ago that if I had to guess and check it meant I’d missed something in class. I remember my teacher in fifth grade trying to get us to guess and check to figure out a simple linear algebra equation. I was the only one who got it right, and that was because my grandpa had taught me a little algebra by that time. (and that got me moved up to the most advanced math class.)
In fact, I think tedium is the enemy of math learning. I think a lot of the problem in math is making kids do problem after problem of the same thing. It takes a while for people who are good at math, and even longer for those that aren’t. Adding a problem like this that is intended to be tedious? I don’t see that helping kids learn math at all.
The type of reasoning needed to do this is rather abstract, and abstract thinking just hasn’t developed in children at this age. Those who say they saw these in sixth and seventh grade make a lot more sense, since that’s around when concrete thinking gives way to abstract thinking. There is a lot of difference in the thinking of children in just a short time.
And I don’t see how these are anything like those logic problems.