Each term is a factorial, 6! = 1 x 2 x 3 x 4 x 5 x 6 = 720.
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Puzzle 3
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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Puzzle 4
How many squares, of any size, are on a board divided up into 6 squares by 6 squares?
