# Math puzzle involving pattern [closed]

This puzzle has been bugging me for quite a few days now. I came across this puzzle in an online website.

2, 4, 1 = 4
3, 1, 6 = 8
7, 2, 4 = 7
1, 0, 8 = ?


Can someone please give a hint. Thanks!

• Why the downvotes? Commented Jul 21, 2022 at 10:00
• Downvotes are probably due to attribution issues. This puzzle may be on topic, but since you clearly stated that you found it online, we require a bit more detail about the source. Commented Jul 21, 2022 at 14:16
• There's a banner along the top of your question with information about how to fix your question. Commented Jul 21, 2022 at 22:39
• oh, ok. it is from an app called Math Riddles Commented Jul 22, 2022 at 13:14

## Hint

The pattern involves 4 operations: addition, concatenation, swapping and one more.

$$9$$
$$\DeclareMathOperator{\swap}{swap}\DeclareMathOperator{\concat}{concat}$$ For numbers $$a, b, c = d$$, we notice that $$\sqrt{a + \concat(\swap(b, c))} = \sqrt{a + \concat(c,b)} = \sqrt{a + 10c + b} = d$$
For the given case, $$\sqrt{1 + \concat(\swap(0, 8))} = \sqrt{1 + \concat(8, 0)} = \sqrt{1 + 80} = \sqrt{81} = 9$$ This pattern is consistent with the listed numbers: \begin{align} \sqrt{2 + \concat(\swap(4, 1))} = \sqrt{2 + \concat(1, 4)} = \sqrt{2 + 14} &= \sqrt{16} = 4\\ \sqrt{3 + \concat(\swap(1, 6))} = \sqrt{3 + \concat(6, 1)} = \sqrt{3 + 61} &= \sqrt{64} = 8\\ \sqrt{7 + \concat(\swap(2, 4))} = \sqrt{7 + \concat(4, 2)} = \sqrt{7 + 42} &= \sqrt{49} = 7\\ \end{align}