Puzzle 65
How many squares of any size on this chessboard do not contain a rook?
Puzzle Copyright © Kevin Stone
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Hint
How many 2 x 2 squares are there?
Answer
There are 128 squares without a rook.
Reasoning
There are 62 squares of size 1 x 1.
There are 41 squares of size 2 x 2.
There are 18 squares of size 3 x 3.
There are 6 squares of size 4 x 4.
There is 1 square of size 5 x 5.
Giving a total of 62 + 41 + 18 + 6 + 1 = 128 squares.
Puzzle 66
If four kittens can catch four toys in four minutes…
…how many toys can twelve kittens catch in twelve minutes?
Puzzle Copyright © Kevin Stone
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Hint
How many toys can one kitten catch in twelve minutes?
Answer
36 toys.
Reasoning
Four kittens can catch four toys in four minutes,
so
one kitten can catch one toy in four minutes,
so
one kitten can catch three toys in twelve minutes,
so
twelve kittens can catch 36 toys in twelve minutes.
Puzzle 67
Using all of the letters A to Z, each once only, complete these common words.
ban-
-a-i-et
-aiz-
s--th
na-e-
-eco-
-ocu-
-la-e
--nk
f-x
be--re
e-ui-
ot-er
wis-
-oast
Puzzle Copyright © Kevin Stone
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Hint
The 2nd word begins with the letter C.
Answers
ban- = bank (K)
-a-i-et = cabinet (CBN)
-aiz- = maize (ME)
s--th = sixth (IX)
na-e- = navel (VL)
-eco- = decoy (DY)
-ocu- = focus (FS)
-la-e = glaze (GZ)
--nk = junk (JU)
f-x = fox (O)
be--re = beware (WA)
e-ui- = equip (QP)
ot-er = otter (T)
wis- = wish (H)
-oast = roast (R)
This puzzle isn't guaranteed to have a unique answer, can you find another?
Puzzle 68
I recently travelled from my home town to a distant music concert, on a pedal tricycle, of all things! My wonderful, three-wheeled tricycle.
I knew that the epic 2,345 mile trip would wreak havoc on the tyres, but luckily I took along 4 spares!
Instead of waiting for any single tyre to fail, I decided that I would rotate the tyres evenly, making sure that by the end of the trip, all seven tyres had travelled exactly the same distance.
What was the distance that each tyre travelled?
Puzzle Copyright © Kevin Stone
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Hint
How many tyre miles were travelled?
Answer
1,005 miles.
Reasoning
A total of 2,345 miles were travelled and at any one time, three tyres were on the tricycle.
Therefore, 3 x 2,345 = 7,035 tyre miles were travelled, which was shared equally by the 7 tyres.
And 7,035 ÷ 7 = 1,005.
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