Puzzle 1
What four-digit number has...
...Digit 2 smaller than Digit 4 which is two thirds of Digit 1 which is two thirds of Digit 3 which is three times Digit 2?
Puzzle Copyright © Kevin Stone
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Hint
Look at Digit 3 first.
Answer
6394.
Reasoning
Labelling the clues:
Digit 2 is smaller than Digit 4
Digit 4 is two thirds of Digit 1
Digit 1 is two thirds of Digit 3
Digit 3 is three times Digit 2
Using (4), Digit 3 can only be 3, 6 or 9 (as it's 3 x Digit 2).
Therefore, using (4), Digit 2 can only be 1, 2 or 3.
Using (3), Digit 1 can only be 2, 4 or 6 (as it's two thirds of Digit 3).
However, using (2), the only possible value for Digit 1 that we can find two thirds of is 6.
So, using (2), Digit 4 is 4.
So far, we have 6??4.
Using (3), Digit 1 is two thirds of Digit 3, so Digit 3 must be 9.
And, by (4), Digit 2 must be 3.
Giving 6394.
Puzzle 2
I recently asked my friend Alex to buy me some ribbon for my child's bonnet.
Alex went to the haberdashery shop for the required length, but accidentally swapped the feet and inches.
When I measured the resulting ribbon, I only had 5÷8 of the length I required.
How much ribbon did I originally ask for?
Remember that there are 12 inches in a foot.
Puzzle Copyright © Kevin Stone
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Hint
A little bit of algebra might help.
Answer
I asked for 7 feet, 4 inches and Alex brought me 4 feet, 7 inches.
Reasoning
If we label what I asked for as A feet and B inches, which is (12 x A + B) inches, then I actually received B feet and A inches, which is (12 x B + A) inches. Which means that:
(5 ÷ 8) x (12 x A + B) = (12 x B + A)
Simplifying gives:
A = (91 ÷ 52) x B
As B is the number of inches, it can only be between 1 and 12 and must give A as a whole number of feet.
B = 4 is the only possible value, which means that A = 7.
So I originally asked for 7 feet, 4 inches.
Double-Checking
I received 4 feet, 7 inches = 55 inches.
I asked for 7 feet, 4 inches = 88 inches, and 88 x (5 ÷ 8) = 55.
Puzzle 3
Sports Day - Logic Puzzles
During the recent BrainBashers school sports day, four students were competing in the 400 metres hurdles. Official figures mysteriously went missing just after the event, however, various spectators could remember the following information. Glen was never suspected though!
Alex won and wore red.
The student wearing number 1 came third.
Blake beat the student in yellow, but wasn't wearing number 2.
Only one student finished in the same position as the number they wore, but they didn't wear red.
Emery beat the student wearing number 3 and Glen wore yellow.
The student in green wore number 2.
A spectator remembered that one student wore blue, but couldn't remember anything else about them.
Can you determine the positions the students finished in, along with the numbers and colours they wore?
Puzzle Copyright © Kevin Stone
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Answer
# Name Wore Colour
1 Alex 4 red
2 Emery 2 green
3 Blake 1 blue
4 Glen 3 yellow
Blake wasn't wearing 2 (clue 3) so wasn't wearing green (clue 6), Alex was wearing red (clue 1) and Glen wore yellow (clue 5), hence Blake wore blue, leaving Emery wearing green wearing 2 (clue 6). As Emery wore 2, and didn't come 3rd (clue 2), and Alex came first (clue 1), which means that Emery must have come 2nd in order to beat the student wearing 3 (clue 5). We now know Alex won and Emery was 2nd, therefore Blake must have come 3rd in order to beat the student in yellow (clue 3), leaving Glen in last place. As Emery came second and beat the student wearing 3 (clue 5), the student wearing 3 must have come 4th (therefore Glen) as the student wearing 1 came 3rd (clue 2). Blake (who is 3rd) wore 1 (clue 2), leaving Alex wearing 4.
Puzzle 4
Jake has some unusual likes and dislikes.
He likes balloons, but does not like parties!
He likes books, but does not like reading!
He likes weeds, but does not like flowers!
He likes swimming, but does not like water!
Does he like towns or villages?
Puzzle Copyright © Kevin Stone
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Hint
Jake also likes skiing.
Answer
Villages.
He only likes words that contain a double letter.
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