Reasoning
These are the squares of numbers without the correct spacing.
1 4 9 16 25 36 49 64 81 100
with no spaces becomes:
149162536496481100
broken into blocks of two:
14 91 62 53 64 96 48 11 00
So the next two in the sequence are 48 and 11.
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Puzzle 2
Can you find the country hidden in the following paragraph?
Aliens landed in downtown Chicago last night. Most locals stepped outside to see the spaceship's massive wingspan. Amazingly, seven people failed to see the sight before them, as they took shelter from the bright light that shone from above.
Aliens landed in downtown Chicago last night. Most locals stepped outside to see the spaceship's massive wingsPAN. AMAzingly, seven people failed to see the sight before them, as they took shelter from the bright light that shone from above.
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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
The map below shows the street locations of a city. Position three police officers such that the entire length of every street can be seen by at least one officer.
