BrainBashers - Mathematical Puzzles

Puzzle 165

Which is larger:

square feet in half a square mile cubic yards in a cubic furlong

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Puzzle 166

How many times can you take 7 away from 49?

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Puzzle 167

A Proof That 2 = 1. Let A = B:

           A = B

multiply by A on both sides:

         A x A = A x B

subtract B x B from both sides:

   A x A − B x B = A x B − B x B

factorise:

  (A + B)(A − B) = B(A − B)

divide by (A − B) on both sides:

       (A + B) = B

replace A with B:

         B + B = B

factorise:

          2B = B

divide by B on both sides:

           2 = 1

Where lies the flaw in the logic?

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Puzzle 168

What is the smallest positive integer which …

… when multiplied by 3 gives a number consisting of only 4's?

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