Puzzle 1
Last week, I travelled from London to Stoke.
On the first day, I travelled one half of the distance.
On day two, I travelled one third of the remaining distance.
On day three, I travelled three quarters of the remaining distance.
Yesterday I travelled one half of the remaining distance.
I now have 5 miles left to travel.
How far is it from Stoke to London in total?
Puzzle Copyright © Kevin Stone
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Hint
Try working backwards.
Answer
120 miles.
Reasoning
I now have 5 miles left to travel, so I must have travelled 5 miles yesterday.
At the end of Day 3, I had 10 miles left to travel, so I must have had 40 miles left at the start of the Day 3.
At the end of Day 2, I had 40 miles left to travel, so I must have had 60 miles left at the start of the Day 2.
At the end of Day 1, I had 60 miles left to travel, so I must have had 120 miles left at the start of the Day 1.
Double-Checking
On the Day 1, I travelled 60 miles, leaving 60 miles.
On Day 2, I travelled 20 miles, leaving 40 miles.
On Day 3, I travelled 30 miles, leaving 10 miles.
Yesterday, I travelled 5 miles, leaving 5 miles.
Puzzle 2
What is made from nothing …
… yet you can see it?
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Hint
Think about it carefully.
Answer
A hole, or a shadow.
Puzzle 3
At the local racetrack, Alex was testing the latest car.
During the eight test laps, Alex managed to average the first two laps at 100mph, the next two laps at 102mph, the next two laps at 140mph, and the last two laps at 150mph.
What was the average speed for the entire 8 laps?
Puzzle Copyright © Kevin Stone
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Share link: https://www.brainbashers.com/ puzzle/zbip
Hint
Remember that Time = Distance ÷ Speed, and try setting the track length to be a random length.
Answer
119mph.
Reasoning
It doesn't matter how long a lap is, so let's set the track length to be a random number, say 5 miles.
Using:
Time = Distance ÷ Speed
The first two laps took:
10 /100 hours
The second two laps took:
10 /102 hours
The next two laps took:
10 /140 hours
The final two laps took:
10 /150 hours
Therefore, the total time for the 8 laps was:
10 /100 + 10 /102 + 10 /140 + 10 /150 hours
= 1 /10 + 5 /51 + 1 /14 + 1 /15 hours
Looking at the denominators:
10 = 2 x 5
51 = 3 x 17
14 = 2 x 7
15 = 3 x 5
The lowest common multiple (LCM) of these numbers is 2 x 3 x 5 x 7 x 17 = 3570.
= 357 /3570 + 350 /3570 + 255 /3570 + 238 /3570 hours
= 1200 /3570 hours
= 120 /357 hours
= 40 /119 hours
The 8 laps were 40 miles, and using Speed = Distance ÷ Time:
average speed = 40 ÷ (40 /119 )
average speed = 40 x (119 /40 )
= 119 mph
Puzzle 4
Below is a very special grid, around each shaded number are 8 white squares.
However, each white square should have a number from 1 to 7.
Once filled in, these 8 numbers will sum to the shaded number.
In addition, once completed correctly, no row nor column will contain a duplicate number within a white square.
For example, the top row may be 5 6 4 2 3 1 7, etc.
This is a very difficult puzzle, and many people resort to using a computer to help them, which is a challenge in itself.
Puzzle Copyright © Kevin Stone
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Share link: https://www.brainbashers.com/ puzzle/ziwb
Hint
This puzzle almost certainly requires trial-and-error to solve, and there is more than one solution.
Answer
There are a number of correct solutions, this is just one of them.
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