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Puzzle 1
How many squares of any size on this chessboard do not contain a rook?
Reasoning 61 squares of size 1 x 1 39 squares of size 2 x 2 20 squares of size 3 x 3 5 squares of size 4 x 4
Giving a total of 61 + 39 + 20 + 5 = 125 squares.
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Puzzle 2
Alex and Billie were rowing their canoe along the River Trent.
In the morning, they managed to row upstream at an average speed of 2 miles per hour.
They then stopped for a spot of lunch and a nice rest.
In the afternoon, the pace was a little easier as they were now rowing downstream back to their starting point, and managed an average speed of 4 miles an hour.
The morning trip took them 3 hours longer than the afternoon.
Hint
You can either fix the distance rowed and see what numbers work, or you can fix the number of hours.
Answer
12 miles.
In the morning, rowing at 2 miles per hour, they rowed for 6 hours. In the afternoon, rowing at 4 miles per hour, they rowed for 3 hours.
There are a number of ways of working this out, and here are two of them:
Method 1
If we assume the distance the rowed upstream to be D miles, we know the morning took (D ÷ 2) hours, and the afternoon took (D ÷ 4) hours, with a difference of 3 hours. So:
D D
- − - = 3
2 4
Multiplying throughout by 4 gives:
2D − D = 12
So:
D = 12 miles
They rowed 12 miles upstream.
Method 2
If we assume they rowed for H hours upstream, we know they travelled H x 2 miles in the morning. In the afternoon, they rowed for (H − 3) hours, and travelled (H − 3) x 4 miles. We know these distances are the same, so:
2H = (H − 3) x 4
Giving:
2H = 4H − 12
Rearranging gives:
12 = 2H
So:
H = 6 hours
They rowed for 6 hours upstream at 2 miles per hour, which is a total of 12 miles.
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Puzzle 3
Focus on this conundrum, do it quickly, or do it slowly. What is so wrong with it? Or so right? It is a most odd conundrum. A quick brown fox jumps, hops, and vaults past a lazy dog! Can you work out what it is? Don't skip any words, and you'll soon spot it. It isn't too hard!
It is now four years since I first asked for support, and I would like to sincerely thank everyone who has helped me. BrainBashers doesn't show adverts, and I continue to depend on the ongoing support from everyone who enjoys the site.
