Puzzle 1
What is the 20th prime number?
2, 3, 5, 7, …
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Hint
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, …
Answer
71.
The first twenty prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.
Puzzle 2
Each of these words can be split in half, and two letters can be placed in the middle to create a new six-letter word.
The four added pairs of letters, in order, spell an 8-letter word. What is that word?
lend
liar
pale
coin
For example:
door + ct = do + ct + or = doctor
suit + nl = su + nl + it = sunlit
Puzzle Copyright © Kevin Stone
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Hint
The 8-letter word begins with the letter G.
Answer
Generous.
lend + ge = le + ge + nd = legend
liar + ne = li + ne + ar = linear
pale + ro = pa + ro + le = parole
coin + us = co + us + in = cousin
Puzzle 3
Imagine a bottle recycling skip, empty other than one lonely bottle.
Every hour, on the hour, people come and put bottles into the skip.
The first hour, at noon, one person came and put a bottle in.
One hour later, two people each placed a bottle into the skip.
An hour later, four people each placed a bottle into the skip.
This doubling of people continued until 11pm, when the skip was finally full.
When was the skip exactly half full?
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Hint
Remember that the bottle count doubles each time.
Answer
10pm.
Reasoning
The skip started with 1 lonely bottle.
At Noon: 1 person came along and added a bottle, making the total 2 bottles.
At 1pm: 2 people came along and each added a bottle, making the total 2 + 2 = 4 bottles.
At 2pm: 4 people came along and each added a bottle, making the total 4 + 4 = 8 bottles.
At 3pm: 8 people came along and each added a bottle, making the total 8 + 8 = 16 bottles.
Therefore, the number of bottles in the skip is doubling every hour, as it was full at 11pm, it must have been half full at 10pm.
Puzzle 4
What is the next number in the sequence:
32 · 35 · 40 · 44 · 52 · 112 · ?
Puzzle Copyright © Kevin Stone
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Hint
This is a tricky question related to number bases.
Answer
200.
Each number in the sequence is a representation of the number 32 in different bases, starting with base 10.
Base 10: 32 = 3 x 10^1 + 2 x 10^0 = 3 x 10 + 2 = 32
Base 9 : 35 = 3 x 9^1 + 5 x 9^0 = 3 x 9 + 5 = 32
Base 8 : 40 = 4 x 8^1 + 0 x 8^0 = 4 x 8 + 0 = 32
Base 7 : 44 = 4 x 7^1 + 4 x 7^0 = 4 x 7 + 4 = 32
Base 6 : 52 = 5 x 6^1 + 2 x 6^0 = 5 x 6 + 2 = 32
Base 5 : 112 = 1 x 5^2 + 1 x 5^1 + 2 x 5^0 = 1 x 25 + 1 x 5 + 2 = 32
Base 4 : 200 = 2 x 4^2 + 0 x 4^1 + 0 x 4^0 = 2 x 16 + 0 + 0 = 32
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