Puzzle 117
The following words have had their vowels removed, can you find the missing animals?
slth
rcn
mnky
llgtr
lphnt
lnd
gt
br
bbn
cyt
Puzzle Copyright © Kevin Stone
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Hint
One of the words is GOAT.
Answer
slth = sloth
rcn = racoon
mnky = monkey
llgtr = alligator
lphnt = elephant
lnd = eland
gt = goat (or agouti)
br = bear (or boar)
bbn = baboon
cyt = coyote
Puzzle 118
Last week I decided to cycle to my Grandparents's house.
On the 1st day, I cycled half of the distance.
On the 2nd day, I cycled one half of the remaining distance.
On the 3rd day, I cycled three quarters of the remaining distance.
On the 4th day, I cycled 10 miles.
On the 5th day, I cycled two thirds of the remaining distance.
On the final day, I cycled the remaining 5 miles.
How far is it to my Grandparent's house?
Puzzle Copyright © Kevin Stone
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Hint
Try working backwards.
Answer
400 miles.
Reasoning
Working backwards:
On the final day I cycled the remaining 5 miles
On Day 5, I started with 15 miles (as I cycled two thirds, leaving 5 miles).
On Day 4, I started with 25 miles (as I cycled 10 miles).
On Day 3, I started with 100 miles (as I cycled three quarters, leaving 25 miles).
On Day 2, I started with 200 miles (as I cycled half, leaving 100 miles).
On Day 1, I started with 400 miles (as I cycled half, leaving 200 miles).
Puzzle 119
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
Puzzle 120
If one small rabbit can dig a warren in nine hours, a medium rabbit can dig a warren in 6 hours, and a large rabbit can dig a warren in four and a half hours.
How long will it take one small, one medium and one large rabbit to dig a warren if they all work together?
Puzzle Copyright © Kevin Stone
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Hint
How much of a warren each rabbit dig in one hour?
Answer
2 hours.
Reasoning
The small rabbit can dig a warren in nine hours, so digs 1/9 in one hour.
The medium rabbit can dig a warren in 6 hours, so digs 1/6 in one hour.
The large rabbit can dig a warren in four and a half hours, so digs 1/4.5 in one hour.
1 Hour = 1/9 + 1/6 + 1/4.5
To make the denominators all the same, we can multiply through by 18/18 to give:
1 Hour = 2/18 + 3/18 + 4/18
1 Hour = 9/18
1 Hour = 1/2
So in one hour, they have dug half a warren, the whole warren will therefore take 2 hours.
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