Puzzle 729
What letter comes next in this sequence:
A · O · E · A · O · T · F · ?
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Hint
This is quite a common representation of the alphabet.
Answer
L.
The last letter from hoteL, which is H in the phonetic alphabet, alphA, bravO, charliE, etc.
Puzzle 730
Can you find a word that is singular, and when you add an 's' it becomes plural, and adding another 's' makes it singular again?
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Hint
One of answers involves royalty.
Answer
Prince, princes, princess.
Bra, bras, brass.
A similar change is care, cares, caress, but these are not nouns.
Puzzle 731
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 732
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.
