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Your goal here is to make me look dumb. Take heart. My nearest and dearest assure me that this task is within the reach of a not particularly bright coral polyp.

Reading the original is not necessary for this problem but if you are interested, it is here. In the original the object was to guess a sequence of three natural numbers between 1 and 100 based on the following information: the numbers were found in contiguous cells in a row of a correctly completed sudoku, and they spelled a three letter word in ASCII in which each letter was of a different case from the one before.

If you work the above out, you will find multiple solutions. The solution set is surprisingly small but not small enough. I reduced the solution set to one by a further restriction that I have never been happy with. I gave some thought to what the final restriction should have been but I was discouraged because it would not be possible to ask the question here.

I believe it is within the scope of this community to ask the following: what is the smallest set of restrictions you can think of that, added to the conditions above will yield a unique solution. In keeping with the spirit of the original, your restrictions (ideally a single restriction) should not mention a specific number and should be something that a mathematical idiot might plausibly remember. An example of what I mean here is that a mathematical idiot might remember "none of the numbers had any of those nasty sharp corners" but definitely not "the numbers were pairwise prime". Find the ideal final condition that I couldn't.

The most elegant solution at the end of a week wins. I read the guidelines and believe that this fits. Doubtless I will be informed if I am mistaken. My hope is that answering this question will help us to learn to be better puzzlers.

Addendum:

The final restriction in the original puzzle was that "there was no way" the heirs could forget the word and I placed the word in each of their names. That left me thinking why I bothered with the sudoku thing in the first place. When it says that Uncle Mort circled part of a row in a sudoku, it sounds as if we're hardly getting any information at all. But if you look at the ascii table (here for example) the restriction of no zeros or repeated digits and alternating case rules out anything in octal or decimal representation. We are left with hex and j-p and J-P are eliminated right off the bat. No letters with repeated digits like D=44 or f=66. If the first letter is in the A-I range the last must be in the Q-Z range. We are close, but not close enough. What reasonable restriction added to the above gives us a unique solution?

Example:
A good restriction would be one that appears to give almost no information like: "I remember Uncle Mort pointed to the box where the first three numbers were and told me the other numbers in the box were the day and year some movie guy died. No idea who.'" (Thanks to Manshu for the idea.)

You don't know the who died, you don't know the day, you don't know anything... or do you? If the person who died was a movie star he couldn't have died before 1900. He couldn't have died later than 1987 because there can't be repeated digits or a 0 in the year (sudoku restriction). Therefore, we know that none of the first three digits can be a 1 or a 9.

We also know that the day can't have a 0, 1 or 9 in it. The wording suggests that the day and year are expressed by the six other digits, four for the year and two for the day. The day must then be in the range from 23 to 28, so none of the first 3 digits in the solution can be a 2.

Dang! Wish I'd thought of this at the time!

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  • $\begingroup$ The linked puzzle has exactly one answer. This answer is marked accepted and it narrows the possibilities to one word based on the original puzzle wording. It is unclear to me what you are asking in this puzzle. $\endgroup$ – Ian MacDonald Mar 7 '16 at 23:29
  • $\begingroup$ @IanMacDonald If i get his question correct then i think he is saying "I gave three clues to find the answer. But what if wanted to give just one. How could I frame the sentence to have the unique answer?" $\endgroup$ – manshu Mar 8 '16 at 6:41
  • $\begingroup$ I guess I wasn't that clear. I put in an addendum that I hope will help. $\endgroup$ – Hugh Meyers Mar 8 '16 at 8:00
  • $\begingroup$ I think that the problem I have with the way this question is posed is that the "the above" in "added to the above" are not clear to me. Just make bullet points and say "which final rule can be added to these to make the solution unique?". $\endgroup$ – Ian MacDonald Mar 8 '16 at 12:40
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    $\begingroup$ @manshu The question is what restriction "added to the conditions above" that is, sudoku and ascii word with alternating case would yield a unique solution. $\endgroup$ – Hugh Meyers Mar 9 '16 at 11:03
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So i limited it to two restrictions.

Restrictions: Absolute value between hex ascii values is 3, Letters are in alphabetical order. For example the number 41 or 47 would be acceptable because abs(4-1)=3 and abs(1-4)=3. There are only 7 letters that meet this condition.

  • A:41
  • G:47
  • R:52
  • X:58
  • c:63
  • i:69
  • t:74

With these letters the only word that meets the original restrictions and the new restrictions is AiR.

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It could be something like

Chelsea: I remember once I was watching a movie with him named "The Seven Year Itch" and when the lead actress died, he said "now there's no way you can forget this".

The interpretation is

Main actress of "The Seven Year Itch" is Marilyn Monroe. She died on August 5, 1962. So the code is 851962

You can also add the name of the country from which the Uncle Mort belongs so that you can clear the confusion between 58**** and 85****

NOTE: I haven't seen the movie. So I am not sure if there is even a death scene or not but I took this just for the sake of the example.

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