Each term alternates between a square and a cube, 8 3 = 512.
?
Puzzle 130
Can you find a 5-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 (larger − smaller) between the first digit and the fourth digit.
Don't forget that 1 isn't prime, as 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
The initial letters form the word ECLIPSE, so any animal beginning with E will work.
??
Puzzle 132
At a recent motorsport gathering, four proud owners were gathered around the silver sports car, each discussing their pride and joy.
Alex was overheard bragging about his brand new Stellar. The person whose surname was Smith went to great lengths to explain to Billie the virtues of his blue Lunar. The person whose surname was Wilshaw, and Dale, were already good friends. The person whose surname was Richards showed everyone a recent photo of his red Orbital. The person whose surname was Stone listened intently while Charlie kept talking about his green Galactic.
Who owns which car?
Reasoning
By (2) the Lunar was Blue, and was owned by Mr Smith.
By (4) the Orbital was Red, and was owned by Mr Richards.
By (5) the Galactic was Green, and was owned by Charlie.
Therefore the Stellar was silver, and by (1) was owned by Alex. Smith Blue Lunar RichardsRed Orbital Charlie Green Galactic Alex Silver Stellar
By (2), Mr Smith wasn't called Billie, so it must have been Billie Richards, and Dale Smith.
By (5) Mr Stone wasn't called Charlie, so it must have been Charlie Wilshaw, and Alex Stone. Dale Smith Blue Lunar Billie RichardsRed Orbital Charlie Wilshaw Green Galactic Alex Stone Silver Stellar
