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I came across this puzzle in an app called Math Riddles.

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

Please give a hint.

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1 Answer 1

5
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Hint

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

Answer

The answer is

$9$

because

$\DeclareMathOperator{\swap}{swap}\DeclareMathOperator{\concat}{concat}$ 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}

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    $\begingroup$ @bobble As a new user on this site, I wasn’t aware. Thanks for the heads up, will keep that in mind for the future. $\endgroup$
    – user80184
    Commented Jul 21, 2022 at 22:39

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