The Lemon Fool

This puzzle was created by Nob Yoshigahara. If you know the answer, it would be considerate to allow others to try to work it out.

What number replaces the question mark?

72    99
  \  /
   27    45
     \  /
      18    39
        \  /
         21    36
           \  /
             ?    28
              \  /
               13    21
                 \  /
                   7

Cheers,

Julian F. G. W.

Are you sure you mean 7 at the bottom?

robbelg wrote:Are you sure you mean 7 at the bottom?

I assume you're thinking that it should be 8 at the bottom, in which case a reasonable answer would be 15. But with 7 at the bottom, there is also a reasonable answer, which I've worked out, and it isn't 15.

No guarantees of course that it's the only reasonable answer - there could in principle be a dozen or more... ;-)

Gengulphus

Gengulphus wrote:

robbelg wrote:Are you sure you mean 7 at the bottom?

I assume you're thinking that it should be 8 at the bottom, in which case a reasonable answer would be 15. But with 7 at the bottom, there is also a reasonable answer, which I've worked out, and it isn't 15.

No guarantees of course that it's the only reasonable answer - there could in principle be a dozen or more... ;-)

Gengulphus

The 7 is correct (otherwise it would be too easy!) and you are correct in saying that the answer is not 15.

The author, Nob Yoshigahara, had one particular answer in mind but I would be interested in any others.

Julian F. G. W.

I love this puzzle, and shall say no more.

Gengulphus wrote:

robbelg wrote:Are you sure you mean 7 at the bottom?

I assume you're thinking that it should be 8 at the bottom, in which case a reasonable answer would be 15. But with 7 at the bottom, there is also a reasonable answer, which I've worked out, and it isn't 15.

No guarantees of course that it's the only reasonable answer - there could in principle be a dozen or more... ;-)

Gengulphus

That's the point where you post clues.

Clue 1: the 15 is obviously a red herring. It's a bit more than that: it appears to be designed to mislead the mind into looking for a different but similar solution.

Clue 2: The tree is a bit more directional than the red herring would have you think. Consider it with little arrows pointing downwards on every arc.

Not-Clue 3: As Gengulphus says, there may be multiple solutions. If what my clues point to isn't the intended one, that could be yet another red herring. Anyone have a good recipe?

One way to tackle a problem is to break it into pieces then put it back together

The intended answer is like a well written crossword clue, when you see it you will know it, and probably kick yourself in the shins for not seeing it earlier.

BobbyD wrote:The intended answer is like a well written crossword clue, when you see it you will know it, and probably kick yourself in the shins for not seeing it earlier.

Don't think I'd kick myself for failing to get a crossword clue. An arcane skill whose utility is obscure, and not one I've ever felt motivated to learn.

p.s. Should post number [n] in this thread be the Great Reveal?

Thanks for posting the puzzle, I've been giving it a go, no luck yet. I know I've seen this puzzle and the solution before but of course I can't remember it.

RC

UncleEbenezer wrote:That's the point where you post clues.

That's the point at which I did post a very obscured clue! ;-) Only a clue as to what the answer is, though, not why it's the answer.

If you want another clue, look at what the various entries in the 'tree' are divisible by. That won't give you the complete pattern, but there's enough of a pattern to it to hopefully set you on the right track.

Gengulphus

jfgw wrote:What number replaces the question mark?
.

OK, here goes one.

robbieg wrote:Are you sure you mean 7 at the bottom?

It makes for a better class of clue, too.

Gengulphus wrote:No guarantees of course that it's the only reasonable answer - there could in principle be a dozen or more

Well, I'd hate to contradict you. Your thinking is free.

UncleEbenezer wrote:That's the point where you post clues.

And do the terrible clues (and not-clues) add up?

In the light of the above, do you think we have arrived?

Gengulphus wrote:
If you want another clue, look at what the various entries in the 'tree' are divisible by. That won't give you the complete pattern, but there's enough of a pattern to it to hopefully set you on the right track.

Gengulphus

That is completely irrelevant to the correct answer

John

redsturgeon wrote:

Gengulphus wrote:If you want another clue, look at what the various entries in the 'tree' are divisible by. That won't give you the complete pattern, but there's enough of a pattern to it to hopefully set you on the right track.

That is completely irrelevant to the correct answer

Being relevant to the correct answer and setting you on the right track to it are not the same thing!

Gengulphus

Would an appropriate clue, given the tree-themed quiz, be to perhaps 'count the leaves'?

Itsallaguess

redsturgeon wrote:

Gengulphus wrote:
If you want another clue, look at what the various entries in the 'tree' are divisible by. That won't give you the complete pattern, but there's enough of a pattern to it to hopefully set you on the right track.

Gengulphus

That is completely irrelevant to the correct answer

John

Not entirely irrelevant. Some numbers have certain properties.

There is also a non-mathematical interpretation.

Itsallaguess wrote:Would an appropriate clue, given the tree-themed quiz, be to perhaps 'count the leaves'?

Itsallaguess

The clues are getting easier.

Julian F. G. W.

I suspect that most of you know the answer by now. Shall I post another clue or shall I just sum up how the problem is solved?

Julian F. G. W.

Itsallaguess wrote:Would an appropriate clue, given the tree-themed quiz, be to perhaps 'count the leaves'?

Itsallaguess

I'd have gone down the sometimes you can't see the tree for the woods route.

8 at the bottom right?

jfgw wrote:I suspect that most of you know the answer by now. Shall I post another clue or shall I just sum up how the problem is solved?

Julian F. G. W.

Go for it Julian. I was on the verge of giving up a couple of days ago when it finally clicked into place.

Cheers,
StepOne