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Find the missing number as indicated by the question mark. Note: the last number, 34, is not a typo.

             48         90
             42         72
             30         54
             24         55
             ?          67
             36         71
             34

Find the missing number. Note: a sequence may conform to more than one rule.

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  • $\begingroup$ Hi Hexomino. Thanks for making the attempt. Because this is a number puzzle, there cannot be a correct rule that leads to a discrepancy. The correct rule is such that it applies exactly to every number. That is why I emphasised that the last number, 34, is not a typo. 71 - 36 = 35, not 34, but 34 is the correct number, not a typo, so your answer is wrong. If you think about it a bit harder, I am sure you will find the right answer. That is, you are on the right track when you connect the two numbers in any row with the first number of the number pair next down the page. Cheers, Laurence $\endgroup$ Nov 13, 2021 at 18:19

3 Answers 3

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I think the answer is

31

Reasoning

Each number on the right is the sum of the number on the left and the one below it.
90 = 48 + 42
72 = 42 + 30
54 = 30 + 24
55 = 24 + 31
67 = 31 + 36
71 = 36 + 34 + 1
There is an extra 1 here at the end which must come from some deeper reasoning.

It seems the difference here is that

71 is the only number in the right column which does not have a number below it so we could modify the formula as follows,
Each number in the right column is the number directly to the left plus the number down and to the left plus 1 minus the number of numbers directly below.

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  • $\begingroup$ No, 31 is not the right answer. See the solved example I gave to Dolan. They did not display as a column, for some reason, so write them as a column. The first pair is 18 39, then 21 36 below, and so on. I'll try again to display them as a column. 18 39 21 36 ? 28 13 21 7 $\endgroup$ Nov 14, 2021 at 7:28
  • $\begingroup$ No, it did not work. I wrote them as a column but they displayed in a line. $\endgroup$ Nov 14, 2021 at 7:29
  • $\begingroup$ Time to show the solution, but I'll hold off for a few hours in case anyone wants to try to find the solution. for themselves $\endgroup$ Nov 14, 2021 at 9:02
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Pretty much just expanding @hexomino's answer

The answer is

30

And the pattern is

The number on the right is the sum of (1) the number on the left in the same line + (2) the number below the latter + 1 if (2)>(1)
90 = 48 + 42
72 = 42 + 30
54 = 30 + 24
55 = 24 + 30 + 1
67 = 30 + 36 + 1
71 = 36 + 34 + 1

Perhaps there's a more elegant answer, but the question does say

A sequence may conform to more than one rule.

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  • $\begingroup$ Hi Dotan,. You mean that the missing number is 30 + 1 =31, but then the last number would not be 34. You are trying to modify the rule that you and Hexomino have found. It can't work. It's the wrong rule. It works only for the first entries, but the right rule will work for all of them. Hers is a simple solved example.. $\endgroup$ Nov 13, 2021 at 19:44
  • $\begingroup$ 18 39 21 36 ? 28 13 21 7 $\endgroup$ Nov 13, 2021 at 20:20
  • $\begingroup$ Sorry Dolan. The numbers are not being displayed in column form. Can you write them down in pairs in a column? The answer is not 15. It is 12. Each number on the left is the sum of the digits of the number pair above. Now try the original puzzle again. Cheers, Laurence $\endgroup$ Nov 13, 2021 at 20:24
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each number in the left hand column, apart from the first, is twice the sum of the digits of the number pair above. Since the number pair above the question mark is 24 55, this gives 2+4+5+5 = 16 and 2 x 16 = 32.

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    $\begingroup$ Is this meant to be an answer, posting the solution to your own puzzle? Or is it more in the way of a hint or clarification, which should be posted as a comment or edit to the question? $\endgroup$ Nov 14, 2021 at 17:15
  • $\begingroup$ Hi Rand'al Thor, I'm new to this, so bear with me. Yes, I gave the solution to my own puzzle. Is that against the rules? I like making them up, but I assumed that this one would be easily solved. Apparently not. If you answer my question I'll carry on posting puzzles but perhaps keep dropping hints rather than give direct solutions. Cheers, Laurence $\endgroup$ Nov 14, 2021 at 20:05
  • $\begingroup$ You can check How long should I wait before providing the answer to my riddle? for some guidance. It's very rare on this site that someone would post the answer to their own puzzle; hints are usually preferred, and there are other options too, as listed in the above-linked meta post and the others shown in the "Linked" sidebar of that question on meta. $\endgroup$ Nov 14, 2021 at 20:12
  • $\begingroup$ This answer doesn't provide a direct answer to the question, i.e. what the missing number is. Could you perhaps edit that in? Note you can hide text in a "spoiler" using >! before it $\endgroup$
    – bobble
    Nov 14, 2021 at 22:22
  • $\begingroup$ Hi bobble. Thanks for that. I'll do as you suggest. Cheers, Laurence $\endgroup$ Nov 15, 2021 at 7:54

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