Puzzle 37
You can replace the dashes with the same four-letter word, and create two new words, one that starts with ARM, and one that ends in ING.
Can you find all possible four-letter words that work?
arm----
----ing
Puzzle Copyright © Kevin Stone
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Hint
There are 4 possible answers.
Answer
Band, load, lock, and rest, all create new words:
armband and banding
armload and loading
armlock and locking
armrest and resting
Note
Some dictionaries also allow ARMRACK, but others don't. So RACK is an unofficial possible answer.
Puzzle 38
In the following line, cross out nine letters such that the remaining letters spell a well-known animal.
e n i l n e e p l e t h t a e n r s t
Puzzle Copyright © Kevin Stone
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Hint
Simply cross out nine letters!
Answer
Elephant.
Cross out the letters 'nine letters' to leave the letters 'elephant'.
Puzzle 39
Yesterday I went for a short bicycle ride around the local lakes. As the weather was very hot, I rode in shorter stages than I'd normally ride.
In Stage One, I rode half of the overall distance.
Stage Two saw half of the remaining distance plus 35 metres covered.
Stage Three covered three-quarters of the remaining distance.
Stage Four completed half of the remaining distance, plus 75 metres.
Stage Five completed the journey with a final burst of 150 metres.
How far did I cycle in total?
Puzzle Copyright © Kevin Stone
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Hint
Try working backwards.
Answer
7,340 metres.
Reasoning
Stage 5's clue tells us that 150m was left. So the distance left at the start of Stage 4 must have been:
Dist4 = Dist4 + 75 + 150
—————
2
Which simplifies to give Dist4 = 450m.
Stage 3's clue tells us that 450m was one quarter of the remaining distance, so Dist3 = 1,800m.
Stage 2's clue tells us that the distance at the start of Stage 2 was:
Dist2 = Dist2 + 35 + 1800
—————
2
Which simplifies to give Dist2 = 3,670m.
Stage 1's clue tells us that 3,670m was half the overall distance, which means the entire ride was 7,340m.
Double-Checking
Starting with 7,340m:
Stage 1: cycled 3,670m, leaving 3,670m
Stage 2: cycled 1,870m, leaving 1,800m
Stage 3: cycled 1,350m, leaving 450m
Stage 4: cycled 300m, leaving 150m
Stage 5: cycled 150m, leaving 0m
Puzzle 40
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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