Puzzle 117
What are the next two numbers in this sequence:
14 91 62 53 64 96 {?} {?}
Puzzle Copyright © Kevin Stone
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Hint
Try removing the spaces between the numbers.
Answer
48 and 11.
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.
Puzzle 118
Using all of the letters A to Z, each once only, complete these common words.
cl--h
co--h
di-r-
-rea-
in-e-
-ok-r
-a-or
-ua-l
re-e-
-to-e
s-am-
ya--t
-eb-a
Puzzle Copyright © Kevin Stone
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Hint
The 4th word begins with the letter F.
Answers
cl--h = cloth (OT)
co--h = cough (UG)
di-r- = diary (AY)
-rea- = freak (FK)
in-e- = index (DX)
-ok-r = joker (JE)
-a-or = manor (MN)
-ua-l = quail (QI)
re-e- = rebel (BL)
-to-e = stove (SV)
s-am- = swamp (WP)
ya--t = yacht (CH)
-eb-a = zebra (ZR)
This puzzle isn't guaranteed to have a unique answer, can you find another?
Puzzle 119
This year, Farmer Stone's harvest of apples was quite significant.
He decided to donate some of the apples to the local community, 1,672 people in all.
Every person aged 50 or more received 16 apples, and every person under 50 received 96 apples.
Only 3/4 of the over 50s collected their apples, and only 1/8 of the under 50s collected theirs.
How many apples did the farmer give away?
Puzzle Copyright © Kevin Stone
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Hint
Try a random number of over 50s to see what happens.
Answer
20,064 apples.
Reasoning
As only 3/4 of the over 50s claimed 16 apples, this averages out to 12 apples each.
Similarly, only 1/8 of the under 50s claimed 96 apples, this again averages out to be 12 apples each.
Therefore, the total number of apples was 1,672 x 12 = 20,064.
It doesn't matter how many over / under 50s there are.
Puzzle 120
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.
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