# impossible math problemJanuary 18, 2012 6:40 AM   Subscribe

Help me figure out what is going on in this image.

It's apparently part of a series of ads from the 50s or 60s (I looked up at one point when exactly Martin was absorbed, but I've forgotten it). The other ads are NOT puzzles and this one appears to be. It even has a clue.

However, the puzzle does not seem solvable as presented. First of all, considering both colors and shapes, there are more than 10 symbols. Assuming each symbol is a digit, we must discard color as being meaningful.

If you try to work it out on that basis, there are still multiple problems. Let's consider the simplest one, which is the first subtraction step (actually, there are two problems here):
``` PPPP
- NPN
-----
RQ
```
(Where P = pawn, N = (k)night, R = rook and Q = queen).

Let me quickly get the second problem with this step out of the way: After the subtraction is done, a pawn must be "pulled down" but when it is it apparently morphs into a rook. So rook and pawn are the same digit? That's odd, but not impossible.

But here's the major problem with that step. We have a 4 digit number minus a 3 digit number with a 2 digit result. The second number must be a palindrome and the middle digit is the same as all the digits in the 4 digit number. Can we do this? What's the very smallest we can get this difference to be? That would be if P = 1 and N = 9. Then we have:
``` 1111
- 919
-----
192
```
That isn't two digits and there's no way to get a smaller answer. (Well, you could have P = 0, but then the whole thing is pointless.) OK, but maybe the pawn-to-rook morph mentioned above means that pieces don't represent particular, unchanging digits. I.e. maybe PPPP is something like 1234. But in that case, is the problem solvable? It doesn't seem like there would be enough information to go on.

Another theory is that the image isn't actually a puzzle, but merely something that looks like a puzzle to attract attention. However, while a person who would make something that looks like a puzzle but is not a puzzle is annoying, a person who would also give a hint about that non-puzzle is just plain evil.

1) That this problem represents some old-timey way of doing long division and I'm making assumptions about certain steps that aren't true. I've looked into this and couldn't find anything. And even so, I think they still did a subtraction step in the ~50s-60s, which is the problem I've highlighted.

2) That this ad started out as a puzzle but somewhere in the path from puzzologist to print it got broken, while the clue remained attached. For instance, maybe a graphic designer thought it looked better if the entire dividend was a single symbol. There are digit alignment issues that could hint towards that, although those problems don't seem to alter the meaning of the puzzle.
posted by DU to Science & Nature (8 answers total) 10 users marked this as a favorite

First of all, considering both colors and shapes, there are more than 10 symbols. Assuming each symbol is a digit, we must discard color as being meaningful.

This is true only if you are working in base 10, which is not an assumption I would make with regards to a math puzzle.
posted by Jairus at 6:57 AM on January 18, 2012

Response by poster: Oh ho ho!

*begins scribbling furiously*
posted by DU at 6:58 AM on January 18, 2012

posted by XMLicious at 7:00 AM on January 18, 2012 [2 favorites]

This has been solved, it seems: http://blog.paddlefish.net/?p=285
posted by hudders at 7:00 AM on January 18, 2012 [1 favorite]

Response by poster: No wait. There's other reasons for discarding color. For instance, look at the end, after the second subtraction. First of all, it appears two pawns have been pulled down at once and not just because of the alignment. Second, the orange pawns have turned into purple pawns. Although if an orange pawn can turn into a green rook then why not a purple pawn and still have color being meaningful.
posted by DU at 7:01 AM on January 18, 2012 [1 favorite]

Response by poster:
OK, but maybe the pawn-to-rook morph mentioned above means that pieces don't represent particular, unchanging digits. I.e. maybe PPPP is something like 1234. But in that case, is the problem solvable? It doesn't seem like there would be enough information to go on.
I didn't think of the above until I'd typed that far and I knew when I did that it would be my downfall. Damn.
posted by DU at 7:03 AM on January 18, 2012

FYI the image has been blacked out for SOPA, so you probably won't get any new answers here for the next 24 hours or so at least.
posted by lollusc at 3:06 PM on January 18, 2012

If it's important, therre's a button to see the image anyway
posted by Redhush at 6:36 PM on January 18, 2012

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