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There is a mathematical puzzle I saw this morning that I am having trouble with.

Seemed easy initially but couldn't crack the code. Can anybody please help work out the answer for the below?

Given the following pattern, find out 1) What is the mathematical formula used to derive the number of the right from the number on the left? 2) What number can be derived from 100 when applying the same formula?

2 => -1

3 => -2

6 => 3

8 => 3

14 => 6

16 => 9

20 => 14

22 => 13

37 => 26

40 => 35

48 => 38

50 => 45

51 => 43

56 => 48

58 => 48

60 => 55

61 => 53

91 => 82

100 => ?

101 => 88

Chilaxis
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    the question after the edit is completely different lol – Asinomás Aug 26 '16 at 03:10
  • haha.. yeah first time using stackexchange, didn't notice that the line-breaks weren't working in the first post! Thanks for having a look at my little puzzle :-) – Chilaxis Aug 26 '16 at 03:15
  • don't you have access to more values? – Asinomás Aug 26 '16 at 03:53
  • One more just came in - 37 => 26. It's actually an office "get-to-know each other" puzzle game. Each gets a pair of number, and we have to introduce ourselves to another one to get a new pair of number :) – Chilaxis Aug 26 '16 at 03:56
  • but you are sure it has an actual pattern right? – Asinomás Aug 26 '16 at 03:58
  • I'm very sure, the puzzle provider gave us the assurance there is a formula used. – Chilaxis Aug 26 '16 at 03:59
  • Trivial observation: $n-f(n)\in {1,2,3,4,5,6,7,8,9,10}$ – Asinomás Aug 26 '16 at 04:04
  • Not true with the 37 => 26 pair though.. got a new one from a colleague : 101 => 88 – Chilaxis Aug 26 '16 at 04:07
  • Can you add all of the pairs to the main post once you get all of them? – suomynonA Aug 26 '16 at 04:09
  • Yup will try to do that, updated with the latest pair. – Chilaxis Aug 26 '16 at 04:11
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    $100$ maps to $90$.

    It appears that the last digit of each number corresponds to what the next step is.

    For example, we have $6$ and $8$ have a difference of $0$, and $56$ and $58$ have a difference of $0$. Similarly, $50$ to $51$ has the same difference as $60$ to $61$, which is $-2$. So, if $101$ is $88$, it must be that $100$ is $90$.

    For fun, I gathered a few relations:

    $0$ to $1$ is $-2$ ; $2$ to $3$ is $-2$ ; $6$ to $7$ is $-2$ ; $7$ to $8$ is $2$

     – Bonnaduck Aug 26 '16 at 04:25
  • Thanks for the observation Bonnaduck. I get that 0 to 1 is −2 ; 2 to 3 is −2 ; But how is it that 6 to 7 is −2 and 7 to 8 is 2 ? – Chilaxis Aug 26 '16 at 05:09
  • There are an infinite number of functions which satisfy all the given values and produce different values for 100. – rikhavshah Aug 26 '16 at 05:28
  • OK - but what would be one of these functions, user125261? :) Bonnaduck and Anonymous' responses converge to 90 being the answer. I will update this post once the office's resident puzzle-master reveals the function he has in mind. – Chilaxis Aug 26 '16 at 05:45
  • @Chilaxis since 6 to 8 is 0, it must be that 6 to 7 is -(7 to 8). Since 7 to 0 is 9, and 8 to 0 is 7, we have 7 to 8 is 2, so 6 to 7 is -2. – Bonnaduck Aug 26 '16 at 19:03

1 Answers1

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I graphed it here. It seems pretty linear, and if you make a line of best fit, 100 would correspond to about 90. Although I can't seem to figure out the algorithm, hopefully the graph helps.

suomynonA
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