# A simple but most devious sequence puzzle

This is a question from a previous, now-defunct version of the Temple of Quetzalcoatl, that I've posted here as an exemplar of one of the difficult puzzles you might encounter while solving it.

The puzzle is simply this:

1845
6745
0738
0956
????

What four-digit number goes into the question marks?

A hint in the source code was presented as such:

-1

• So many ideas...so many things to try... Is the solution obvious when you see it? Mar 28, 2015 at 1:23
• Yes, it is. Very obvious. Otherwise the puzzle wouldn't be so much evil as it would be unclear and unfair.
– user88
Mar 28, 2015 at 1:27
• Not digging for too much of a hint, but can you do this without cultural/historical/etc knowledge? I'm not much good with dates and statistics, but if it's mostly logic and lateral thinking I'll keep mulling it over... Mar 28, 2015 at 9:09
• There are no dates or statistics in the puzzle, nor are any of them involved in the solution.
– user88
Mar 28, 2015 at 18:05
• However, Google may be of use, as many of the problems in the Temple were intended to involve a little bit of research.
– user88
Mar 28, 2015 at 18:26

1617

Explanation:

264 = 18,446,744,073,709,551,616

This could be written as

1844 6744 0737 0955 1616

Then you just

Add 1 to each of the numbers to get the numbers on the list, so the missing number is 1617

• I have no idea how you could have possibly figured that out. Bravo. Mar 29, 2015 at 9:41
• That's exactly it. Good job figuring this out in less than two days.
– user88
Mar 29, 2015 at 10:02
• I guess it's quite easy if you've memorised enough powers of 2... Mar 29, 2015 at 11:16
• This specific power of 2 is relatively notable as the answer to a problem involving grains of wheat and a chessboard.
– user88
Mar 29, 2015 at 17:13
• Really? I'm disappointed by this being the solution. This was arbitrary and unclued, and the only way I imagine reaching it is by trying loads of equally arbitrary and unclued thing, or getting lucky. A clue at digits or powers of 2 or concatenation would have given some direction.
– xnor
Mar 29, 2015 at 21:10

9745

Explanation

These are guesses made by someone in the cows-and-bulls game. In the first step, they got two bulls so they decided to change two numbers to see which positions are right. They got three bulls in the next step meaning that the digits kept fixed were right and one of the other digits was too. So they decided to keep one digit and two unseen digits in other places to figure out the fourth digit. They should have got one bull meaning that 7 was right and the other digits were all wrong. This left only 2 and 9 as possibilities for the first digit and hence they played a move with 9 and previously seen digits. They got a cow and thus the answer is 9745. this should be played in the last step to win.

• Good guess, and very creative explanation (+1), but the pattern of the sequence has nothing to do with Mastermind.
– user88
Mar 29, 2015 at 8:19

Each digit should appear twice, so I'm thinking of twice the missing digit and once each of one and nine.

I just don't find a logical sequence for the 4 digits.

• 5 appears three times in the existing numbers.
– user88
Mar 29, 2015 at 4:11
• ... and 3 appears only once. Mar 29, 2015 at 11:14