BrainBashers - Random Puzzles

Puzzle 1

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 2

In the illustration we have a sketch of Sir Edwyn de Tudor going to rescue his love, who was held captive by a neighbouring wicked baron.

Sir Edwyn calculated that if he rode at fifteen miles an hour he would arrive at the castle an hour too soon, while if he rode at ten miles an hour he would get there just an hour too late.

Now, it was of the first importance that he should arrive at the exact time appointed, in order that the rescue that he had planned should be a success, and the time of the tryst was five o'clock, when the captive would be taking afternoon tea.

The puzzle is to discover exactly how far Sir Edwyn de Tudor had to ride.

Sir Edwyn De Tudor, Amusements In Mathematics, Henry Ernest Dudeney.

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Puzzle 3

Gardener's Spring Fayre – Logic Puzzles

At the recent spring fayre, four keen gardeners were displaying their fine roses.

In total there were four colours and each rose colour appeared twice.

From the clues below, can you tell who had which colour roses?

Gardener Green had a yellow rose.
Gardener Yellow did not have a red one.
Gardener Red had a blue rose, but not a green one.
Gardener Blue did not have a yellow one.
One person with a red rose also had a green one.
One person with a yellow rose also had a blue one.
One of the persons with a green rose had no red.
Neither of the persons with a yellow rose had a green one.
No person had two roses of the same colour.
No two persons had the same two colour roses, and their names provide no clues.

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Puzzle 4

Jam Making Contest – Logic Puzzles

At the recent interdepartmental jam making contest, four lucky candidates took part to make the juiciest strawberry jam.

As it happens, the person who came last was the oldest.
Glen was three years older than the person who came second.
Drew was neither the oldest nor the youngest.
Emery finished ahead of the 27-year-old, but didn't win.
Alex was also unlucky this time, and didn't win either.
The ages of the contestants were 24, 27, 30 and 32.

Can you work out who finished where, and how old they were?

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