Puzzle 725
What is the smallest positive integer which …
… when multiplied by 3 gives a number consisting of only 4's?
Puzzle Copyright © Kevin Stone
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Hint
Try working backwards.
Answer
148.
Reasoning
A number that is divisible by 3 has digits that add up to a number that is also divisible by 3 (for example, 123 is divisible by 3).
So we can look for the first number where 4 + 4 + 4 + 4 + 4 + … is divisible by 3, which is 4 + 4 + 4, and 444 ÷ 3 = 148.
Alternative Reasoning
Let's try the possible answers in order:
4 ÷ 3 = 1.3333
44 ÷ 3 = 14.6666
444 ÷ 3 = 148
Double-Checking
148 x 3 = 444.
Puzzle 726
What letter is missing from this sequence:
A B G D E ? E
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Hint
This is quite a common alphabet.
Answer
Z.
From Zeta, first letters of the Greek alphabet, alpha, beta, gamma, delta, epsilon, zeta, eta.
Puzzle 728
What is the 10th prime number?
2, 3, 5, 7, …
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Hint
2, 3, 5, 7, 11, 13, 17, 19, 23, …
Answer
29.
The first ten prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
