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1, 6, 5, 3, 4, 1, 2, 2, ?

Hint: the task is pattern recognition using basic mathematical operations.

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  • $\begingroup$ Has a correct answer been given? If so, please don't forget to $\color{green}{\checkmark \small\text{Accept}}$ it :) $\endgroup$
    – Rubio
    Oct 11, 2017 at 14:32
  • $\begingroup$ s this pattern the result of a series based on a starting rule that is then used to construct the rest of the series? Like a Fibonacci series? Or is this a pattern that you arbitrarily dreamed up according to a rule that cannot start a series? – $\endgroup$
    – Dr t
    Oct 18, 2017 at 18:14

3 Answers 3

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I guess:

The answer is 0. Every third number is the difference between the previous 2 numbers.

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    $\begingroup$ the only issue i take with an answer like this is, it breaks up the single sequence into individual sequences of 3 entries. However, I like the answer as it answers the question. $\endgroup$
    – Jason V
    Oct 5, 2017 at 13:53
  • $\begingroup$ Is this pattern the result of a series based on a starting rule that is then used to construct the rest of the series? Like a Fibonacci series? Or is this a pattern that you arbitrarily dreamed up according to a rule that cannot start a series? $\endgroup$
    – Dr t
    Oct 18, 2017 at 18:13
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If I have to solve this question, you can do this.

Subtract the first number from the second number. 6- 1 = 5, 4 - 3 = 1 , 2 - 2 = 0

so, the series would be

(1, 6, 5), (3, 4, 1), (2, 2, 0)...
Now after 0, the number would be 1.
Adding the triplets and dividing by 4, we get the next number.
See, (1 + 6 + 5)/4 = 3,
(3 + 4 + 1)/4 = 2,
(2 + 2 + 0)/4 = 1

so, the series now would be

(1, 6, 5), (3, 4, 1), (2, 2, 0), 1
And then the next number in the series would be 0
Check the middle number of the triplets, it decreases by 2.
6, 4, 2 and then comes 0

so, the series would be

(1, 6, 5), (3, 4, 1), (2, 2, 0), (1, 0, -1), (0, -2, -2), .........

I hope I answered your question.

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If we can separate the unique sequence into three sequences of three numbers (165 341 22?), then perhaps the pattern can also be:

1 6 5

3 4 1 -

2 2 4

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  • $\begingroup$ Why 224 specifically though? $\endgroup$ Apr 6, 2019 at 20:42
  • $\begingroup$ Is a subtraction calculation between the first sequence of three numbers and the second one: 165 - 341 = 224. 4 would be the answer. $\endgroup$
    – user58413
    Apr 6, 2019 at 21:22
  • $\begingroup$ But 165 - 341 is -176, not 224 ... $\endgroup$ Apr 7, 2019 at 5:02
  • $\begingroup$ They are sequences, not three-digit numbers. consider the units separately. for example, instead of 165, read one, six, and five. what I propose is the subtraction calculation between the last number of the first sequence (1 6 5) and the last number of the second sequence (3 4 1) to arrive at the third number of the last sequence (2 2 4), since the pattern seems to be repeated in relation to the first two numbers of each sequence: 1 - 3 = 2, 6 - 4 = 2. 5 - 1 = 4. $\endgroup$
    – user58413
    Apr 7, 2019 at 15:46

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