Reasoning
In 36 hours, Alex could empty 2 lots of bookshelves, Billie could also empty 2 lots of bookshelves, and Drew could refill 1 lot of bookshelves.
So, 2 + 2 − 1 = 3 lots of bookshelves in 36 hours. Which is 12 hours for one lot of bookshelves.
Alternative Reasoning
Alex and Billie can each empty 1/18 of the bookshelves in 1 hour, but Drew will refill 1/36 of the bookshelves in one hour.
So in one hour we have 1/18 + 1/18 − 1/36 = 1/12.
So it would take 12 hours to empty the bookshelves.
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Puzzle 226
Can you find a five-digit number that …
… if you place a 9 at the beginning is four times larger than if you place a 9 at the end instead?
Hint
Adding 900,000 to the numbner is the same as placing a 9 at the beginning.
Answer
23,076.
Reasoning
Placing the 9 at the beginning is equivalent to adding 900,000 (for example, 12,345 + 900,000 becomes 912,345).
Placing the 9 at the end is equivalent to multiplying by 10 and adding 9 (for example, 12,345 x 10 + 9 becomes 123,459).
Let's call the unknown number k, and we know that one of these numbers is 4 times the other, so:
k + 900,000 = 4 x (10k + 9)
k + 900,000 = 40k + 36
900,000 − 36 = 40k − k
899,964 = 39k
899,964 ÷ 39 = k
Therefore, k = 23,076.
Double-Checking 923,076 = 4 x 230,769.
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Puzzle 227
My first is in camel, and in hamster.
My second is in otter, but not in ferret.
My third is in mustang, but not in horse.
My fourth is in snake, and in asp.
My last is in tiger, and in panther.
Reasoning
My first is in camel, and in hamster = AEM
My second is in otter, but not in ferret = O
My third is in mustang, but not in horse = AGMNTU
My fourth is in snake, and in asp = AS
My last is in tiger, and in panther = ERT
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Puzzle 228
A well-known seven-letter word can be created, by starting with a single letter and adding a letter, one at a time, then mixing the letters, each time making a proper word. Using the clues below, which are not necessarily in the correct order, can you find all seven words? For example, A, AT, TAR, RATE, etc.
Expressing position within limits of space and time. The subject of self-consciousness. Frozen atmospheric vapour falling to earth. To utter musical sounds with the voice. Cause to oscillate. Scattering on the earth. The breaking of divine law.
Hint
The longest word is the answer to 'Frozen atmospheric vapour falling to earth'.
Answers
Snowing, sowing, swing, sing, sin, in, I.
snowing – frozen atmospheric vapour falling to earth
sowing – scattering on the earth
swing – cause to oscillate
sing – to utter musical sounds with the voice
sin – the breaking of divine law
in – expressing position within limits of space and time
I – the subject of self-consciousness
