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Oct 1, 2015 at 10:44 comment added dr_ @KBusc If you solve the equations you'll see that this is the only solution. You can find other values that hold true if you consider a smaller subset of numbers (e.g. from 1 to 10 safes).
Oct 1, 2015 at 7:25 comment added Christoph @SeraphCheng I added some explanation
Oct 1, 2015 at 7:24 history edited Christoph CC BY-SA 3.0
added 1258 characters in body
Oct 1, 2015 at 6:07 comment added Saurabh Prajapati after reading all comments and thinking for two an hour , i still unable to understand the answer. can you please explain more and step by step please.
Sep 30, 2015 at 19:42 comment added KBusc Any proof that this is the ONLY solution? I'm not convinced this is unique.
Sep 30, 2015 at 18:20 comment added S.C. Excellent. How did you get to this solution?
Sep 30, 2015 at 15:45 comment added Puzzle Prime @dr01, oh I see, it seems you have changed it from 36 to 25 since the previous time I checked.
Sep 30, 2015 at 15:09 comment added dr_ @ArturKirkoryan Unfortunately it's not possible to fit 18 in the pattern: T is supposed to be 0 because of EIGHTEEN=EIGHT+TEN, but it was previously set as 11 by other constraints.
Sep 30, 2015 at 15:03 comment added Puzzle Prime @dr01, yeah I guessed that's why you multiplied by 2. Still, it was very close for the system to be unsolvable, which is what makes your problem so nice.
Sep 30, 2015 at 14:57 comment added dr_ @ArturKirkoryan Using the same values works well for numbers up to 10. For bigger numbers, it must be E=0 (because SIXTEEN = SIX+TEN) and I=0 (because THIRTEEN=THREE+TEN). If you're working with the same values, this makes N=4.5 because of NINE=9. The reason I multiplied by 2 was also to have a riddle with only integers.
Sep 30, 2015 at 14:49 comment added Puzzle Prime @dr01, I guessed your system didn't have a solution for ONE=1, TWO=2, etc. due to problems modulo 2 and this is why you multiplied by 2. Now when I think about it though, 14, 16, 17, 19 repeat the digits 4, 6, 7, 9 with added teen at the end, so basically we have 16 degrees of freedom and 16 numbers to encode (1-13+15+18+20), which generally should be possible. Still, the coincidence is interesting and also a bit baffling why you have so many zeros among the letter values.
Sep 30, 2015 at 14:36 comment added dr_ @ArturKirkoryan Thanks. It is not mandatory to multiply by 2. This kind of mathematical recreation (known as neomerology) is usually done with the same values i.e. ONE=1, TWO=2, etc. I just wanted to make a riddle that was somehow different.
Sep 30, 2015 at 14:28 comment added Puzzle Prime @Aioros, after 20 it is not a surprise it works (since "Y" appears for the first time in "twenty" and 0-9 repeat all the time), but it is interesting how with just 16 letters (12 non-zeros) you can get all of the first 20 numbers (I assume this is why the OP had to multiply by 2?). Very nice indeed.
Sep 30, 2015 at 14:22 comment added Aioros Nah, not for me at least. I definitely wouldn't have figured it out all the same.
Sep 30, 2015 at 14:21 comment added dr_ @Aioros Thanks. I apologize again for my error; it slipped somehow during the calculations of the Diophantine equations for the 90 codes. It shouldn't have spoiled too much the riddle.
Sep 30, 2015 at 14:15 comment added Aioros I wanted to say that the error in the original question threw us a bit off and that the number replacements are too weird, but I'm entirely too baffled from seeing that this actually works somehow.
Sep 30, 2015 at 14:05 comment added dr_ Yes, that was it. Congratulations!
Sep 30, 2015 at 14:04 history bounty ended dr_
Sep 30, 2015 at 14:04 vote accept dr_
Sep 30, 2015 at 14:03 history answered Christoph CC BY-SA 3.0