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What are the appropriate numbers in the patterns below:

First pattern

$4\hspace{1cm}14\hspace{1cm}11\hspace{1cm}31$

$35\hspace{0.8cm}26\hspace{1cm}73\hspace{1cm}?$

Second pattern

$7\hspace{1cm}8\hspace{1cm}20\hspace{0.8cm}1$

$5\hspace{1cm}6\hspace{1cm}2\hspace{1cm}?$

Third pattern

$41\hspace{1cm}44\hspace{1cm}72\hspace{1cm}78$

$36\hspace{1cm}66\hspace{1cm}62\hspace{1cm}?$

I have been trying many different ways to look at it, product, sum, factors, multiples and some other combinations but still could not find the missing number. Could anyone please give some hints?

I believe they are not very difficult questions.

Thanks.

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  • $\begingroup$ Are the two lines separate sequences or continued from above, i.e., is the first sequence 4 14 11 31 35 26 73 ? or is 4 14 11 31 an example of the rule and 35 26 73 ? another sequence using the same rule? Or something else, e.g., 4&35 14&26 11&63 31&?? $\endgroup$
    – Arkku
    Commented Apr 20, 2017 at 13:00
  • $\begingroup$ @Arkku I think it should be separate but related, there should be a reason to write in two lines. Another sequence may or may not have the same rule. My guess maybe a different rule. $\endgroup$
    – user71346
    Commented Apr 20, 2017 at 13:20
  • $\begingroup$ Has a correct answer been given? If so, please don't forget to $\color{green}{\checkmark \small\text{Accept}}$ it :) $\endgroup$
    – Rubio ♦
    Commented May 19, 2017 at 5:32

1 Answer 1

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Well, this is easy. And they revolve around the same basic trick.

14 - 4 = 10 and 31-11= 20...That's the trick essentially. Difference has to double for subsequent pairs.For the next sequence, 35 26 73 ?... We easily see 35-26=9 and So we must have difference = 18...So our required number is 55.

The third pattern definitely owes itself to the same logic when we observe :

44-41=3 and 78- 72=6....So easily: 66-36=30...and we must have then x-62=60...and that gives us the required number is 122

The second one also involves the same concept...with a slight twist in arrangement:

7 8 20 1 .... All we need is to observe 7 - 1 = 6 and 20 - 8 = 12. Got our pattern again. So, we see here 6 - 2 = 4...we need to achieve the difference between 5 and x to be 2...and hence our required number is 3.

So, we are seemingly done.

Thank You :)

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  • $\begingroup$ In addition, this sequence is chosen to also have same pattern vertically (so, 73 in the first case and 62 in 3rd cannot be replaced by another number). Except for the second one. This one seems completely arbitrary. And it could be 0.1 too. First too verticals have -2, the last 2 would have /10. About as valid. $\endgroup$
    – Zizy Archer
    Commented Apr 20, 2017 at 14:55
  • $\begingroup$ Yeah. One could have done with a few more terms and you know, like a crispier relation/pattern. $\endgroup$
    – Swarnabja Bhaumik
    Commented Apr 20, 2017 at 15:01

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