## Puzzle 1

**Pre-Championship Rehearsal** - Logic Puzzles

At last month's rehearsal, four top athletes competed in two 400-metre qualifiers.

As the results were expected to be mislaid, various notes were taken to ensure the accuracy of the overall placings:

No one finished both races in the same position.

In both races, Sam beat the runner whose surname was Watson.

Billie Taylor came third in the second race, and Pat came last in the first race.

In the second race, the athlete whose surname was Arnold won, and the athlete whose surname was Bowler came last.

In the first race, Billie beat Jamie, but Jamie beat Sam.

Can you determine who finished where in each of the races?

Puzzle Copyright © Kevin Stone

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Hint

Look at Clue 3 first, and then Clue 5.

Answer

Race1 Race2

————————————————————————

#1 Billie Sam

Taylor Arnold

————————————————————————

#2 Jamie Pat

Bowler Watson

————————————————————————

#3 Sam Billie

Arnold Taylor

————————————————————————

#4 Pat Jamie

Watson Bowler

Reasoning

The four names were: Billie, Jamie, Pat, Sam

The four contestants were: Arnold, Bowler, Taylor, Watson.

By (3), Billie Taylor came third in the second race, and Pat came last in the first race, giving:

Race1 Race2

————————————————————————

#1

————————————————————————

#2

————————————————————————

#3 Billie

Taylor

————————————————————————

#4 Pat

By (5), in the first race Billie beat Jamie, and Jamie beat Sam, giving:

Race1 Race2

————————————————————————

#1 Billie

Taylor

————————————————————————

#2 Jamie

————————————————————————

#3 Sam Billie

Taylor

————————————————————————

#4 Pat

By (2), Sam beat the runner with the surname Watson in the first race, which means that Pat's surname is Watson, giving:

Race1 Race2

————————————————————————

#1 Billie

Taylor

————————————————————————

#2 Jamie

————————————————————————

#3 Sam Billie

Taylor

————————————————————————

#4 Pat

Watson

By (1), Pat can't have also finished in last place in race 2, and by (2), Sam beat the Pat Watson, so Pat must have finished in second place in race 2. And Sam came first, therefore Jamie came last, giving:

Race1 Race2

————————————————————————

#1 Billie Sam

Taylor

————————————————————————

#2 Jamie Pat

Watson

————————————————————————

#3 Sam Billie

Taylor

————————————————————————

#4 Pat Jamie

Watson

By (4), in the second race the athlete whose surname was Arnold won, and the athlete whose surname was Bowler came last, so we know Sam and Jamie's surnames, and we can complete the grid:

Race1 Race2

————————————————————————

#1 Billie Sam

Taylor Arnold

————————————————————————

#2 Jamie Pat

Bowler Watson

————————————————————————

#3 Sam Billie

Arnold Taylor

————————————————————————

#4 Pat Jamie

Watson Bowler

## Puzzle 2

Here we have a rectangular room, measuring 30 feet by 12 feet, and 12 feet high.

There is a spider in the middle of one of the end walls, 1 foot from the ceiling (A).

There is a fly in the middle of the opposite wall, 1 foot from the floor (B).

What is the shortest distance that the spider must **crawl** in order to reach the fly?

The Spider and the Fly – The Canterbury Puzzles, Henry Ernest Dudeney

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Hint

Going down and across the floor isn't the only route.

Answer

40 feet.

Explanation Diagram

If you imagine the room to be a cardboard box, you can 'unfold' the room in various ways, and each route gives a different answer.

We can use Pythagoras' theorem to calculate the distances:

distance^{2} = horizontal^{2} + vertical^{2}

distance = √(horizontal^{2} + vertical^{2})

Route #1

distance = 1 + 30 + 11 = 42 feet.

Route #2

horizontal = 6 + 30 + 6 = 42 feet.

vertical = 10 feet.

distance = √(42^{2} + 10^{2}) ≈ 43.174 feet.

Route #3

horizontal = 1 + 30 + 6 = 37 feet.

vertical = 6 + 11 = 17 feet.

distance = √(37^{2} + 17^{2}) ≈ 43.178 feet.

Route #4

horizontal = 1 + 30 + 1 = 32 feet.

vertical = 6 + 12 + 6 = 24 feet.

distance = √(32^{2} + 24^{2}) = 40 feet.

## Puzzle 3

Below you will find 15 **well-known** six-letter words, with only their endings remaining.

Can you find the words?

---cil
---hid
---nze
---ese
---lug
---som
---uxe
---uum
---arm
---amo
---rby
---ink
---sai
---too
---fen

Puzzle Copyright © Kevin Stone

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Hint

The first letters of the words are: p, o, b, c, u, r, d, v, d, d, n, s, b, t, d.

Answer

---cil = pencil
---hid = orchid
---nze = bronze
---ese = cheese
---lug = unplug
---som = ransom
---uxe = deluxe
---uum = vacuum
---arm = disarm
---amo = dynamo
---rby = nearby
---ink = shrink
---sai = bonsai
---too = tattoo
---fen = deafen

## Puzzle 4

Which country has been hidden in the paragraph below:

The local habitat around a railway track can be very interesting. For example, supporting the track is a sleeper, under which you can find the lesser-spotted great weevil.

Puzzle Copyright © Kevin Stone

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Hint

The country has four letters.

Answer

Peru.

The local habitat around a railway track can be very interesting. For example, supporting the track is a slee**per, u**nder which you can find the lesser-spotted great weevil.

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