Answers
The added letters spell TELESCOPE. herb + t becomes berthbang + e becomes begankeen + l becomes kneelsuit + e becomes suitequad + s becomes squadwhey + c becomes chewycell + o becomes cellotoil + p becomes pilotwild + e becomes wield
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Puzzle 522
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
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Puzzle 523
What four-letter word can be placed between the two following words to make two new words:
table[----]house
In the following example, the word 'book' creates the words 'cookbook' and 'bookcase'.
cook[book]case
