The Lemon Fool

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

The numbers above have been arranged according to a certain rule. What is the value of the missing number x?

Cinelli

I think this has been posted before but annoyingly I cannot remember the answer

RC

ReformedCharacter wrote:I think this has been posted before but annoyingly I cannot remember the answer

RC

Yes, and some of us played silly games and dropped cryptic clues.

But my tortuous answer needs more posts.

Just looked.

Originally posted here by jfgw on May 24th, 2017, with attribution. The first to post a cryptic clue was Gengulphus, just an hour and a half later. Took a bit longer before most of us joined the fun.

I didn't realise this had been posted previously. But it is a marvellous puzzle and I urge all to try for a solution without following UncleEbenezer's link. I will give full attribution with the solution. I tend not to give the source with the problem as it is a temptation to google for an answer.

Cinelli

cinelli wrote:I didn't realise this had been posted previously. But it is a marvellous puzzle and I urge all to try for a solution without following UncleEbenezer's link. I will give full attribution with the solution. I tend not to give the source with the problem as it is a temptation to google for an answer.

Cinelli

I agree, it's a fine puzzle, with that splendid red herring to distract you from an answer that should be more obvious.

I suspect the lack of takers here may be because those of us who might bite remember it from first time round. Or already knew it back then. For myself, I don't think I can improve on my convoluted post number [solution] in that thread.

UncleEbenezer wrote:I agree, it's a fine puzzle, with that splendid red herring to distract you from an answer that should be more obvious.

Thank you for that remark. Got me looking at it differently. The required rule then became quite obvious quite quickly.

UncleEbenezer wrote:Just looked.

Originally posted here by jfgw on May 24th, 2017, with attribution. The first to post a cryptic clue was Gengulphus, just an hour and a half later. Took a bit longer before most of us joined the fun.

I had completely forgotten that I had posted this. I have just worked it out - nothing too complicated.

Julian F. G. W.

For completeness it is high time I gave the solution to this problem, and to give full acknowledgement to its creator, Japanese Nob Yoshigahara who considered it his masterpiece.

It all looks straightforward – each number is the difference of the two above. Except for that pesky 7 at the bottom. Surely that is a mistake? But no. The numbers have been ingeniously chosen so that most satisfy two rules. It is only at the final step that one of the rules fails. The rule which satisfies all steps is to add the digits of the two numbers above. For example 21 = 1 + 8 + 3 + 9. Then x = 2 + 1 + 3 + 6 = 12 and sure enough 1 + 2 + 2 + 8 = 13.

Cinelli