Puzzle 321
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 322
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 323
What is the smallest positive integer, which, when multiplied by 6 …
… gives a number consisting of only 8's?
Puzzle Copyright © Kevin Stone
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Hint
Try working backwards.
Answer
148.
148 x 6 = 888.
The easiest way is to divide successive 8's by 6 until you get an integer:
8 ÷ 6 = 1.3333
88 ÷ 6 = 14.666
888 ÷ 6 = 148
Puzzle 324
Someone purchases 1 for 38p, 23 for 76p and 102 for £1.14.
What are they buying?
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Hint
3,876 would cost £1.52.
Answer
House numbers at 38p each.
