Puzzle 189
Last week, I travelled from Birmingham to Glasgow (via bicycle).
On the first day, I travelled one quarter of the distance.
On day two, I travelled one half of the remaining distance.
On day three, I travelled three quarters of the remaining distance.
Yesterday I travelled one third of the remaining distance.
I now have 21 miles left to travel.
How far is it from Birmingham to Glasgow in total?
Puzzle Copyright © Kevin Stone
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Hint
How many miles were left at the start of yesterday?
Answer
336 miles.
Reasoning
To work these numbers out, it is perhaps easier to start at the end and work backwards.
Yesterday I travelled 1/3 of the distance to leave 21 miles, therefore there were 31.5 miles (=21 ÷ 2/3) at the start of yesterday.
On day 3 I travelled 3/4 of the distance to leave 31.5 miles, therefore there were 126 miles (=31.5 ÷ 1/4) at the start of day 3.
On day 2 I travelled 1/2 of the distance to leave 126 miles, therefore there were 252 miles (=126 ÷ 1/2) at the start of day 2.
On the first day, I travelled 1/4 of the distance to leave 252 miles, therefore there were 336 miles (=252 ÷ 3/4) at the start of the first day.
Double-Checking
On the first day, I travelled one quarter of the distance (84, leaving 252).
On day two, I travelled one half of the remaining distance (126, leaving 126).
On day three, I travelled three quarters of the remaining distance (94.5, leaving 31.5).
Yesterday I travelled one third of the remaining distance (10.5).
I now have 21 miles left to travel.
Puzzle 190
Chess Contest - Logic Puzzles
At the local games evening, four friends were competing in the chess and croquet competitions.
Frankie beat Glen in chess, Dale came third, and the 16-year-old won.
Frankie came second in croquet, the 15-year-old won, Dale beat the 18-year-old, and the 19-year-old came third.
Emery is 3 years younger than Glen.
The person who came last in chess came third in croquet, and only one person got the same position in both games.
Can you find the ages of the people and their positions in the two games?
Puzzle Copyright © Kevin Stone
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Hint
How old could Glen be?
Answer
Name Age Chess Croquet
Dale 15 3 1
Emery 16 1 4
Frankie 18 2 2
Glen 19 4 3
Reasoning
The possible ages are: 15, 16, 18, 19.
Breaking the clues down, and numbering them:
Frankie beat Glen in chess.
Dale came third (chess).
The 16-year-old won (chess).
Frankie came second in croquet.
The 15-year-old won (croquet).
Dale beat the 18-year-old (croquet).
The 19-year-old came third (croquet).
Emery is 3 years younger than Glen.
The person who came last in chess came third in croquet.
Only one person got the same position in both games.
By (4), Frankie came 2nd in croquet.
Name Age Chess Croquet
Dale
Emery
Frankie 2
Glen
By (2), Dale came 3rd in chess.
Name Age Chess Croquet
Dale 3
Emery
Frankie 2
Glen
By (8), Emery is 15 or 16, and Glen is 18 or 19.
By (9), the person who came 4th in chess, came 3rd in croquet, and by (7), they are 19. This can't be Dale (3rd in chess), or Frankie (2nd in croquet), or Emery (aged 15 or 16), so it must be Glen.
Name Age Chess Croquet
Dale 3
Emery
Frankie 2
Glen 19 4 3
By (6), Dale can't have been 4th in croquet, so must be 1st. Leaving Emery in 4th.
Name Age Chess Croquet
Dale 3 1
Emery 4
Frankie 2
Glen 19 4 3
By (10), only one person got the same position in both games, this can't be Emery 4th in both (as Glen is already 4th in chess), so must be Frank, 2nd in both. Leaving Emery 1st in chess.
Name Age Chess Croquet
Dale 3 1
Emery 1 4
Frankie 2 2
Glen 19 4 3
By (3) and (5) we know the ages of the winners in each competition, and Frankie is therefore 18.
Name Age Chess Croquet
Dale 15 3 1
Emery 16 1 4
Frankie 18 2 2
Glen 19 4 3
Puzzle 191
Which of the shapes is identical to the first one?
There might be more than 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.
Puzzle 192
Once you have unscrambled the following countries, the first letters can be anagrammed to make a hidden country.
aadnorr
aehiiopt
ceeegr
aaaacdgmrs
anorwy
aaimnor
eemny
Puzzle Copyright © Kevin Stone
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Hint
One of the answers is Yemen.
Answer
Germany.
Reasoning
aadnorr = Andorra
aehiiopt = Ethiopia
ceeegr = Greece
aaaacdgmrs = Madagascar
anorwy = Norway
aaimnor = Romania
eemny = Yemen
a + e + g + m + n + r + y = Germany.
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