## Puzzle 5

**Training Stars #1** - Logic Puzzles

The first group of trainee astronauts are all sitting around the table, waiting to start their first day of training.

From the clues given below, can work out where everyone sits?

Seat 1 is next to Seat 2 and Seat 8, etc. Seat 5 is across from Seat 1, and Seat 7 is across from Seat 3, etc. Seat 2 is a higher seat number than Seat 1, etc.

William is next to Alisa and Nick.

William is across from George.

Amanda is next to Sarah.

Sarah is across from Eric.

Nick is next to Eric.

Sydney is in Seat 4 and sits next to George.

George has a higher seat number than Sydney.

Alisa is not in Seat 2.

Puzzle Copyright © Randall Fine

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Hint

Where does George sit?

Answer

Seat 1 = William

Seat 2 = Nick

Seat 3 = Eric

Seat 4 = Sydney

Seat 5 = George

Seat 6 = Amanda

Seat 7 = Sarah

Seat 8 = Alisa

Reasoning

Sydney is in Seat 4 and is next to George (Clue 6), so George is in either Seat 3 or Seat 5. But George has a higher seat number than Sydney (Clue 7). Therefore, George is in Seat 5.

William is across from George (Clue 2), and therefore is in Seat 1.

William is next to Alisa and Nick (Clue 1), so Alisa and Nick are in Seat 2 and Seat 8 (either way around). But Alisa is not in Seat 2 (Clue 8). Therefore, Alisa is in Seat 8 and Nick is in Seat 2.

Nick is next to Eric (Clue 5) so can only be in Seat 3.

Sarah is across from Eric (Clue 4), and therefore is in Seat 7.

Amanda is next to Sarah (Clue 3) and can only be in Seat 6.

## Puzzle 6

Below, 10 nine-letter words have been broken into chunks of three letters.

These chunks have been mixed up, no chunk is used twice, and all chunks are used.

Can you determine what the 10 words are?

For example: computing = com + put + ing.

rbr ent ard man tor rbo

and ban con erf dst dli

fly spa dra dif hai ght

per all fis ove ush hea

new gon fer wat her duc

Puzzle Copyright © Kevin Stone

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Hint

These are the first letters of the words: w, o, b, h, d, f, c, n, h, d.

Answer

wat + erf + all = waterfall

ove + rbo + ard = overboard

ban + dst + and = bandstand

hai + rbr + ush = hairbrush

dif + fer + ent = different

fis + her + man = fisherman

con + duc + tor = conductor

new + spa + per = newspaper

hea + dli + ght = headlight

dra + gon + fly = dragonfly

## Puzzle 7

Complete the fifth circle with the correct dots.

Puzzle Copyright © Kevin Stone

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Hint

At each stage a new dot appears at the top.

Answer

At each stage, a new dot starts at the top, and then goes either clockwise, or counter-clockwise.

## Puzzle 8

Three teachers were discussing how long they had been teaching.

Alex and Billie had been teaching for a total of 36 years.

Charlie and Billie had been teaching for a total of 22 years.

Charlie and Alex had been teaching for a total of 28 years.

How long had each been teaching?

Puzzle Copyright © Kevin Stone

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Hint

If we look at all of the clues, each person appears exactly twice.

Answer

Alex had been teaching for 21 years.

Billie had been teaching for 15 years.

Charlie had been teaching for 7 years.

Reasoning

If we look at all of the clues, each person appears exactly twice.

So the total of the three clues gives us two lots of Alex + Billie + Charlie = 36 + 22 + 28 = 86.

So, Alex + Billie + Charlie = 43 years.

In each clue we are given two of the people, so we can use this to find the missing person:

Charlie and Billie had been teaching for a total of 22 years, which means that Alex must be: 43 - 22 = 21 years.

Charlie and Alex had been teaching for a total of 28 years, which means that Billie must be: 43 - 28 = 15 years.

Alex and Billie had been teaching for a total of 36 years, which means that Charlie must be: 43 - 36 = 7 years.

Reasoning With Algebra

Let Alex = A, Billie = B and Charlie = C, then:

[1] A + B = 36

[2] C + B = 22

[3] C + A = 28

If we use [3] - [2] we have:

[4] A - B = 6

If we use [1] + [4] we have:

2A = 42

A = 21

By [1] B = 15. By [3] C = 7.

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