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.
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Puzzle 6
Can you find the country hidden in the following paragraph:
As a keen photographer, I find the best way to capture the portrait of a gazelle is to stand well downwind. I also try to wear clothes that blend in with the background to reduce the chances of scaring the animal.
As a keen photographer, I find the best way to capture the portrait of a gazelle is to stand well downwIND. I Also try to wear clothes that blend in with the background to reduce the chances of scaring the animal.
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Puzzle 7
How many squares are in the drawing below?
Note: this puzzle is not interactive, and the squares cannot be clicked.
In the solution below, you can see 6 squares in the middle, with another 12 squares around the outside.
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Puzzle 8
Can you find a five-digit number that has no zeros, and no repeated digits, where:
The first digit is a prime number. The second digit is the fifth digit minus the first digit. The third digit is twice the first digit. The fourth digit is the third digit plus three. The fifth digit is the difference between the first digit and the fourth digit.
Don't forget that 1 isn't prime, the prime numbers start with 2, 3, 5, …
Hint
Start with the possible answers where the first digit is a prime number, and then look at the third digit.
Answer
23,475.
Reasoning
By (1), the first digit is prime:
2----
3----
5----
7----
By (3), the third digit is twice the first digit, so we can eliminate 5---- and 7----:
2-4--
3-6--
By (4), the fourth digit is the third digit plus three:
2-47-
3-69-
By (5) the fifth digit is the difference between the first digit and the fourth digit:
2-475
3-696
We know from the introduction that no digit is repeated, so we can eliminate 3-696. And, by (2) the second digit is the fifth digit minus the first digit:
23475
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