Puzzle 1
Yesterday I went for a short bicycle ride around the local lakes. As the weather was very hot, I rode in shorter stages than I'd normally ride.
In Stage One, I rode half of the overall distance.
Stage Two saw half of the remaining distance plus 35 metres covered.
Stage Three covered three-quarters of the remaining distance.
Stage Four completed half of the remaining distance, plus 75 metres.
Stage Five completed the journey with a final burst of 150 metres.
How far did I cycle in total?
Puzzle Copyright © Kevin Stone
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Hint
Try working backwards.
Answer
7,340 metres.
Reasoning
Stage 5's clue tells us that 150m was left. So the distance left at the start of Stage 4 must have been:
Dist4 = Dist4 + 75 + 150
—————
2
Which simplifies to give Dist4 = 450m.
Stage 3's clue tells us that 450m was one quarter of the remaining distance, so Dist3 = 1,800m.
Stage 2's clue tells us that the distance at the start of Stage 2 was:
Dist2 = Dist2 + 35 + 1800
—————
2
Which simplifies to give Dist2 = 3,670m.
Stage 1's clue tells us that 3,670m was half the overall distance, which means the entire ride was 7,340m.
Double-Checking
Starting with 7,340m:
Stage 1: cycled 3,670m, leaving 3,670m
Stage 2: cycled 1,870m, leaving 1,800m
Stage 3: cycled 1,350m, leaving 450m
Stage 4: cycled 300m, leaving 150m
Stage 5: cycled 150m, leaving 0m
Puzzle 2
How many squares of any size on this chessboard do not contain a rook?
Puzzle Copyright © Kevin Stone
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Hint
There are no squares of size 5x5.
Answer
There are 125 squares without a rook.
Reasoning
There are 61 squares of size 1x1.
There are 39 squares of size 2x2.
There are 20 squares of size 3x3.
There are 5 squares of size 4x4.
Giving a total of 61 + 39 + 20 + 5 = 125 squares.
Puzzle 3
I recently gave a new watch to my friend for their birthday.
However, as usual with my presents, it was quite useless as it gains 6 minutes every hour.
I set it using my own accurate clock at midnight, and the watch now shows 8:26am.
I know that it stopped 30 minutes ago, so what is the correct time now?
Puzzle Copyright © Kevin Stone
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Hint
How many watch minutes pass in a real hour?
Answer
8:10am.
Reasoning
The watch now shows 8:26am, so we know that 8 x 60 + 26 = 506 watch minutes have passed.
Since the watch is gaining 6 minutes every hour, for every real hour that has passed, the watch will show 66 minutes.
So, 506 ÷ 66 ≈ 7.666 real hours have passed.
This equals 460 minutes, which is 7 hours and 40 minutes = 7:40am.
The watch stopped 30 minutes ago, therefore the time must now be 8:10am.
Puzzle 4
Each of these words has had its vowels (AEIOU) removed.
Can you re-add the vowels and find the related words?
cbbg
clflwr
ccmbr
crgtt
crrt
clrc
Puzzle Copyright © Kevin Stone
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Hint
The words are all vegetables.
Answers
cbbg = cabbage
clflwr = cauliflower
ccmbr = cucumber
crgtt = courgette
crrt = carrot
clrc = celeriac