Puzzle 1
Training Stars #2 all logic puzzles
The second group of trainee astronauts are all sitting around the rectangular table, waiting to start their first day of training.
From the clues given below, can work out where everyone sits?
The seats are numbered clockwise, with Seat 1 next to Seats 2 and 8. Opposite pairs are Seats 1 & 5, 2 & 8, 3 & 7, and 4 & 6.
Harvey has a higher seat number than Jennie.
Peter is across from Harvey.
Neither Joyce nor Lia is in seat 8.
Rick is across from Kenny, and Rick is also next to Joyce.
Lia is next to Kenny.
Jennie is at Seat 4 and next to Harvey.
Peter is next to Lia.
Mark has the remaining seat.
Puzzle Copyright © Randall Fine
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Hint
Where does Harvey sit?
Answer
Seat 1 Peter
Seat 2 Lia
Seat 3 Kenny
Seat 4 Jennie
Seat 5 Harvey
Seat 6 Joyce
Seat 7 Rick
Seat 8 Mark
Reasoning
Jennie is in Seat 4 and next to Harvey (Clue 6), so Harvey is in Seat 3 or Seat 5.
Harvey has a higher seat number than Jennie (Clue 1), so Harvey is in Seat 5.
Peter is across from Harvey (Clue 2), so is in Seat 1.
Peter is next to Lia (Clue 7), so Lia is in Seat 8 or Seat 2. But Lia is not in Seat 8 (Clue 3), therefore Lia is in Seat 2.
Lia is next to Kenny (Clue 5), therefore Kenny must be in Seat 3.
Rick is across from Kenny (Clue 4), so must be in Seat 7.
Joyce is next to Rick (Clue 4), but not in Seat 8 (Clue 3), so Joyce must be in Seat 6.
The last remaining seat (Seat 8) is occupied by Mark (Clue 8).
Puzzle 2
The river Pregel ran through the town of Konigsberg. In the river were two islands, connected to each other and the rest of the city by seven bridges.
The residents of Konigsberg challenged each other to walk through the city, and cross each of the seven bridges exactly once.
Can you find a path that they might have taken?
This is the 'Seven Bridges of Konigsberg' puzzle, tackled by Leonhard Euler in 1736.
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Hint
Try starting in one corner.
Answer
There is no possible route.
Leonhard Euler (1707 to 1783), a Swiss polymath, was the first to prove that this puzzle had no solution.
Puzzle 3
A very long time ago, at the beginning of the week, I was given some money for my birthday.
On Monday, I spent a quarter of the money on clothes.
On Tuesday, I spent one third of the remaining money on music.
On Wednesday, I spent half of the remaining money on games.
Finally, on Thursday, I spent the last £12.50 on a book.
How much birthday money did I receive?
Puzzle Copyright © Kevin Stone
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Hint
It might be easier to work backwards.
Answer
£50.
Reasoning
Working backwards:
On Thursday, I had £12.50.
On Wednesday, I had £12.50 x (1 ÷ one half) = £25.
On Tuesday, I had £25 x (1 ÷ two thirds) = £37.50.
On Monday, I had £37.50 x (1 ÷ three quarters) = £50.
Puzzle 4
Which of the shapes are identical to the first one?
Puzzle Copyright © Robert A. Hartmann
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Hint
Try to rotate them around in your head, but watch out for mirror images.
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