# Multiply!

We haven’t done any recreational math for a while. As a change of pace, instead of the division problems we’ve done in the past, here’s a multiplication problem. The usual rules for this kind of cryptarithm apply:

• Each letter represents one of the digits 0-9.
• Different letters represent different digits.
• There are no leading zeros, so in the problem below we know right away that A, C, D, and FG are not zero.

Unlike many examples of these, if you put the letters for 0-9 in order, it won’t spell anything.

```      A B C
x    D E F
----------
G H I C
G E G B
C G G C
-------------
C D F J I C
```

Please ROT13 any solutions, so others can keep playing.

## 24 thoughts on “Multiply!”

1. Guy says:

I believe you mean A, C, D, and G are nonzero.

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• Guy says:

And, in order of discovery, digits identified by their first three english letters:
O mre P svi N fvk Q ava R rvt T sbh S fri V gue U gjb W bar

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• Alan Scott says:

That’s what I got too, gubhtu V svtherq gurz bhg va gur beqre PONTQRSUVW

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• ian351c says:

I got the same. Behold the power of Excel (lots of MOD and INT functions)! And one really lucky guess. I really have no method to this madness, just the starting clue around C.

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2. veronica d says:

Wouldn’t it be funny if it spelled “something” rather than “anything,” ’cause, you know, Mike Schilling.

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• Mike Schilling says:

Wrong number of letters :-)

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3. veronica d says:

This reminds me, I need to actually learn Prolog someday.

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4. Wyrmnax says:

Aff.

I got a system with plenty of equations on it. Now its just a time to substitute them all.

Btw, “F” is obvious from the very first moment.

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• Mike Schilling says:

How was F obvious to you? The other solvers (and I) didn’t get it until fairly late.

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• X x Y = ZX (To put a finer point on it, a number that ends in X)
X =/= 1

Is where I am currently.

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• Mike Schilling says:

Be K vf rira naq L vf fvk.

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• Wyrmnax says:

Still, it is trivial. It can only be one of two different numbers.

Btw. You should spell a number when you are pointing out it in a rot 13 text.

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• Wyrmnax says:

Or, i can be completely wrong. Wouldn’t be the first time.

Gur bayl jnl n zhygvcyvpngvba bs n ahzore pna erfhyg bs n ynfg qvtvg bs vgfrys ner gurfr:

1 – gur zhygvcyvpngbe vf bar
2 – gur zhygvcyvpngbe vf fvk
3 – Bar bs gubfr ahzoref vf svir naq gur bgure vf bqq.

Jr pna rkpyhqr 1 sebz gur trg tb nf gur erfhyg jbhyq or nop. Gung yrnirf hf jvgu gur ynfg gjb cbffvovyvgvrf. Fb S vf rvgure Fvk, Svir (fbzrguvat ryfr NAQ P vf svir)

Fb creuncf zl vavgvny fgngrzrag jnf vapbeerpg.

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• Alan Scott says:

, V’z thrffvat lbh unir vg jebat, naq lbhe svkngrq ba gur cbffvovyvgl bs S orvat 6. Vg vfa’g.

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5. Glyph says:

God love you all, but the phrase ‘recreational math’ lands on my brain in roughly the same way as ‘salubrious torture’. It just doesn’t (wait for it) add up.

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• Mike Schilling says:

Kind of like ‘rap music’.

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6. Randy Harris says:

Ol wbyyl uvtuynaqf va Trbetvn prqne nfu sybngf rireljurer qnex

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• Alan Scott says:

lrc. Naq V nccebir bs lbhe rapbqvat zrgubq.

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N rfgn frvf, O abguvat, P vf n unaqshyy, Q ahra, R fvqrjnlf vasvavgl, S vf yhpxl, T n fdhner, U vf pbzcnal, V vf n pebjq, naq W havgl.

Vg jnf zhpu rnfvre bapr V ernyvmrq gung P unq gb or svir naq O mreb. Nsgre gung V fnj gung R jnf rira, S naq Q bqq, naq gung Q jnf bar zber guna R. Gura fnj N k Q ybbxrq yvxr vg unq gb or svsgl fbzrguvat juvpu znqr N naq Q rvgure fvk naq 9 be 8 naq 7. Nyy sryy vagb cynpr sebz gurer.

Thanks for the puzzle, I lurves puzzles.

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Got it. Took about a half-hour. C and B were obvious from inspection. But then I had to start writing equations.