Here is a sequence:
1, 2, 4, 7, 8, 11, 14, 16, 17, 19, 22, 26, 28, 29, 41, 44, 46, 47,…

What is the next number in the sequence?

A hint from Sherlock, who said it best in the story “Silver Blaze”:

“Is there any other point to which you would wish to draw my attention?”
“To the curious incident of the dog in the night-time.”
“The dog did nothing in the night-time.”
“That was the curious incident,” remarked Sherlock Holmes.

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So, figured it out yet? XD

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Solution:

49 is the correct answer.

… And there’s a reason why I chose to truncate the sequence where I did and let you puzzle it out. Most textbooks would tell you that the sequence continues thus:

1, 2, 4, 7, 8, 11, 14, 16, 17, 19, 22, 26, 28, 29, 41, 44, 46, 47, 49, 61, 62, 64,…

However, I believe in fairness. If I had asked for, say, the next four numbers in the sequence and was given 49, 52, 56, 58 as an answer, I would accept it.

Why?

As Sherlock said, look for what’s missing; therein lies the rules of how to construct the sequence.

We exclude a number if it has at least one of the following properties:
-multiple of 3
-multiple of 5
-any number containing 3 (ie notice there are no numbers in the thirties listed in the sequence)

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BUT… there could a sneaky fourth rule that you may or may not delineate:
-any number containing 5

Technically some multiples of 5 before the fifties (5, 15, 25, 35, 45) are also numbers containing 5. In my opinion, you could argue either way that this rule is/is not included in what we exclude from the sequence.

So, the fourth rule? Yes or no? ‘Tis the question!

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• Happy New Year’s, Everyone! – from December 31, 2014
• McSpirk Gift Exchange – from December 15, 2014
• This Person Needs Help – from July 25, 2014