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Here's another problem, significantly harder than the first, but still accessible to target audience. The statement of the problem (i.e., northwest corner only) comes from a PennyDell puzzle magazine:

EDIT The problem is described below in the comments; additionally, NTRF is N times OGRE and ONOT is SLOG minus NTRF; the "A" is "brought down" per algorithm. Next two hunks explained similarly.

enter image description here

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  • $\begingroup$ Could you clarify that notation (it seems to be division), which is the divisor and which is the quotient? $\endgroup$ Jul 20 '15 at 1:01
  • $\begingroup$ @YoTengoUnLCD It is surely long division of SLOGAN / OGRE = NET. $\endgroup$ Jul 20 '15 at 2:32
  • $\begingroup$ Oh, thanks. I'd never seen that notation before, it's weird. $\endgroup$ Jul 20 '15 at 2:42
  • $\begingroup$ Heh... like I said here, long division's future is questionable; apparently the notation is English/U.S. only? I wasn't aware of how limited it already IS, let alone how limited in the future in countries that DO use the notation. I can understand why it's foreign to others--it is indeed weird. But it sure does offer some interesting, challenging mathematics. $\endgroup$
    – DSlomer64
    Jul 22 '15 at 15:48
  • $\begingroup$ I've edited the OP to explain. $\endgroup$
    – DSlomer64
    Jul 22 '15 at 16:03
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Thanks for a very nice puzzle. I prefer the long division puzzles over cryptarithms with only addition or multiplication, but I usually find the Feynman puzzles too hard.

Solution:

First clue: O-O = R (in ONOTA-OOOES=RRON) and R not zero give R=9 and N is one more than O.
Then OGRE x E=OOOES give E=8 and S=4.
Therefore 8 x OG + 7 = OOO: Only fit is O=1 and G=3 (because 8 x 13 = 104).

The rest is easy and the numbers are 401352 divided by 1398 is 287 with 126 remaining.

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