# Brain twisting maths sequence question 5

But what is the explanation?

• I think the most 'fun' with these types of puzzles is seeing how many legitimate answers turn up ... – Lamar Latrell Mar 31 at 5:47
• @LamarLatrell oeis.org/… – Servaes Mar 31 at 11:08

5

because

the sequence is the first nine digits of pi - 3.14159265(35...) - written left to right, top to bottom. The colours of the boxes are red herrings.

5. The columns sum to $$6,12,18$$.

• I love it. Right answer, clearly (to me) the wrong explanation. A bronze badge for you. – Ross Millikan Apr 1 at 3:24

Another answer may be found with modular arithmetic.

First row are the sum of columns below mod 10 (or, in a decimal system, the rightmost digit). Though I'm more inclined to the pi digits answer, this one does not require prior knowledge of pi digits but some simple pattern recognition.

1st col: (2 + 1) mod 10 = 3

2nd col: (5 + 6) mod 10 = 1 (since 11 mod 10 = 1)

3rd col: (x + 9) mod 10 = 4 -> x mod 10 = 5 -> x = 5 is the smallest answer.

Downside is that this explanation accepts infinite answers, so long as they hold mod 10 = 5: 5, 15, 25, 124895701235, etc, but it is reasonable to assume that most people will settle on 5, if anything, considering every other number is smaller than 10 (say, they are themselves the result of mod 10).