# What is the next sequence of numbers?

Seven and seven is forty-two,
Eight and nine are fifty;
Ten and eleven are sixty-two,
And twelve and twelve are five.

What is the next sequence of numbers?

• Is there a reason that the first one has an "is" and the rest don't - they have "are"s? Commented Feb 10, 2019 at 23:15
• No clue. I'm sure there are reasons. Or maybe there is a reason. er.... Commented Feb 11, 2019 at 0:54
• @Riddler, Hint? Commented Feb 17, 2019 at 22:28
• It is merely a puzzle :) It is numeric Commented Feb 23, 2019 at 20:19
• Has a correct answer been given? If so, please don't forget to $\color{green}{\checkmark \small\text{Accept}}$ it. If not, some responses to the answerer to help steer them in the right direction would be helpful.
– Rubio
Commented Mar 7, 2019 at 4:43

I think the next line is

Thirteen and fourteen is eighty

Reasoning

After the first line, the first number in each line is one higher than the second number in the previous line. Also, the second number in each line is either the same or one higher than the first number in the same line. Hence, the next line should either be

Thirteen and thirteen is ... or
Thirteen and fourteen is ...

If we analyse the first three lines there is a simple formula which they satisfy, namely

$$X$$ and $$Y$$ is $$4X + 2Y$$

Using this as a starting point and extrapolating to subsequent lines we have the following

$$7$$ and $$7$$ is $$4\times 7 + 2 \times 7 = \textbf{4}2$$
$$8$$ and $$9$$ is $$4\times 8 + 2 \times 9 = \textbf{5}0$$
$$10$$ and $$11$$ is $$4\times 10 + 2 \times 11 = \textbf{6}2$$
$$12$$ and $$12$$ is $$4\times 12 + 2 \times 12 = \textbf{7}2$$

Obviously, this doesn't match the 4th line but we will try to address that later. For the moment, if we analyse the two possibilities for the next line we have

$$13$$ and $$13$$ is $$4 \times 13 + 2 \times 13 = \textbf{7}8$$
$$13$$ and $$14$$ is $$4 \times 13 + 2 \times 14 = \textbf{8}0$$

If we wish to continue the pattern in the tens unit (highlighted in bold) we should choose the latter as the next line of the sequence.

Deviation in the 4th line

As stated previously, the fourth line does not match the formula. My interpretation of this is that "seventy-two" sounds like "seven to two" and the number of integer steps between seven and two is five.

The only reason I can think that the OP would use this interpretation is that the puzzle simplifies a lot otherwise. Equally we could have replaced "sixty-two" by "six to two" which is four.

• Another way to make the 4th line match is to consider results to be modulo 67 ;-) Commented Mar 5, 2019 at 23:24