Logic puzzles, riddles, math puzzles and brainteasers - pzzls.com

Vandaag is het 21 April 2018

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Kid me not - puzzling puzzle

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   Rating: 2.2/5.0

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I cannot be felt, seen or touched;
Yet I can be found in everybody;
My existence is always in debate;
Yet I have my own style of music.
What Am I?

Country puzzle - logic puzzle

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If Costa Rica goes with Thailand, Cuba goes with Puerto Rico, and the Netherlands go with Yugoslavia, what country would the Ivory Coast go with?

2=1? - math puzzle

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Suppose: a = b

It then follows that
a * a = a * b
a^2 = a * b
a^2 - b^2 = a * b - b^2
(a - b) * (a + b) = (a - b) * b
a + b = b
a + a = a
2 * a = 1 * a
2 = 1

Is this derivation really correct? Or is there somewhere a mistake? If so, where?