Puzzle 9
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 10
Can you find the number that best completes this puzzle?
Puzzle Copyright © Kevin Stone
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Hint
The answer involves a square root.
Answer
4.
The middle of each triangle contains the square root of the sum of the three surrounding numbers.
Puzzle 11
During the recent BrainBashers Football Competition, 5 teams were competing.
Each team played each other just once, with 2 points for a win, 1 point for a draw, and 0 points for a loss.
However, the rain damaged the final scoresheet, and this is all that could be read of the final points after all of the matches:
Longton 6
Fenton 5
Blurton 4
Hulton 2
Fulton {?}
Can you work out how many points Fulton ended the season with?
Puzzle Copyright © Kevin Stone
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Hint
How many games took place?
Answer
3.
Reasoning
There were 5 teams in the league, and every team played every other, so there were a total of 10 games played:
Longton vs Fenton
Longton vs Blurton
Longton vs Hulton
Longton vs Fulton
Fenton vs Blurton
Fenton vs Hulton
Fenton vs Fulton
Blurton vs Hulton
Blurton vs Fulton
Hulton vs Fulton
We know that 2 points were allocated for each game played. Which means that there were a total of 20 points over the 10 games.
Since the given results add to 17, the remaining 3 points belong to Fulton.
Puzzle 12
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.
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