Puzzle 225
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?
Puzzle Copyright © Kevin Stone
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Hint
What's a mathematical way to describe 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.
Puzzle 226
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.
What am I?
Puzzle Copyright © Kevin Stone
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Hint
The first letter is M.
Answer
Mouse.
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
Puzzle 227
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.
Puzzle Copyright © Kevin Stone
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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
Puzzle 228
At the local racetrack, Alex was testing the latest car.
During the eight test laps, Alex managed to average the first two laps at 100mph, the next two laps at 102mph, the next two laps at 140mph, and the last two laps at 150mph.
What was the average speed for the entire 8 laps?
Puzzle Copyright © Kevin Stone
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Hint
Remember that Time = Distance ÷ Speed, and try setting the track length to be a random length.
Answer
119mph.
Reasoning
It doesn't matter how long a lap is, so let's set the track length to be a random number, say 5 miles.
Using:
Time = Distance ÷ Speed
The first two laps took:
10/100 hours
The second two laps took:
10/102 hours
The next two laps took:
10/140 hours
The final two laps took:
10/150 hours
Therefore, the total time for the 8 laps was:
10/100 + 10/102 + 10/140 + 10/150 hours
The 8 laps were 40 miles, and using Speed = Distance ÷ Time:
average speed = 40 ÷ (10/100 + 10/102 + 10/140 + 10/150)
= 119 mph
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