BrainBashers - Random Puzzles

Puzzle 57

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 58

Can you complete the grid without forming a 3-In-A-Row of the same colour.

Each row and column has an equal number of Blue and White squares.

This puzzle has been added to the collection of logic puzzles that change daily on BrainBashers. Click the link at the top of the page to see today's puzzles.

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Puzzle 59

My local greengrocer is a would-be mathematician.

She likes to arrange the apples in nice rows.

When she lays the apples in rows of 3, she has one left over.

And, when she lays them in rows of 5, she also has one left over.

Remarkably, she also has one left over when she arranges them in rows of 7 and 9.

But 11 seems to be the magic number, because in rows of 11 there are no apples left over.

How many apples does she have?

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Puzzle 60

Can you find a word that means perimeter …

… and by adding a letter A another word is formed that means a lodger?

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