All in unknown

Logic Level 1

All numbers are integers.

0 < < < \diamondsuit \neq \spadesuit \neq \heartsuit \neq \clubsuit \\ 0\le \clubsuit <\diamondsuit <\spadesuit <\heartsuit

( + ) = ( + ) + = 1 ( + ) = 5 \clubsuit \left( \diamondsuit +\heartsuit \right) =\clubsuit \left( \spadesuit +\heartsuit \right) \\ \diamondsuit +\clubsuit =1\\ \diamondsuit \left( \heartsuit +\spadesuit \right) =5

Find ( + ) + \spadesuit \left( \diamondsuit +\heartsuit \right) +\clubsuit


The answer is 8.

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1 solution

Andrew Levada
May 27, 2018

From ( + ) = ( + ) \clubsuit \left( \diamondsuit +\heartsuit \right) =\clubsuit \left( \spadesuit +\heartsuit \right) you can find out that = 0 \clubsuit =0 or = \diamondsuit =\spadesuit . And you know that \diamondsuit \neq \spadesuit . So = 0 \clubsuit =0 . Also + 0 = 1 = 1 \diamondsuit +0=1\quad \Rightarrow \quad \diamondsuit =1 . And 1 ( + ) = 5 + = 5 1\left( \heartsuit +\spadesuit \right) =5\quad \Rightarrow \quad \heartsuit +\spadesuit =5 . If you check, the only possible value is = 3 = 2 \begin{matrix} \heartsuit =3 & \spadesuit =2 \end{matrix} . After if you count all you'll get 8.

Nowhere does it say that the symbols represent integers, so the split of 5 into 3 and 2 is not the only way to go.

Also \diamondsuit \neq \heartsuit \neq \clubsuit \neq \spadesuit could mean only that , , \diamondsuit \neq \heartsuit, \heartsuit \neq \clubsuit, \clubsuit \neq \spadesuit This does not guarantee that \diamondsuit \neq \spadesuit

Marta Reece - 3 years ago

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I fixed it.

Andrew Levada - 3 years ago

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