Puzzle 1
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 2
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 3
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 4
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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