Reasoning
If we denote Alex by A, Billie by B, Charlie by C, and Drew by D and number the clues.
If Alex had three more sheep, then he'd have one fewer sheep than Billie.Whereas Drew has the same number as the other three shepherds put together.If Charlie had three fewer sheep, he'd have exactly three times the number of Alex.If they were evenly distributed, they'd each have eleven sheep.
By (4): A + B + C + D = 44
And, by (2), these are shared equally between A + B + C and D.
Alex finished after Frankie.Drew finished after Hayden.Frankie finished after Billie.Hayden finished before Alex.Billie finished after Hayden.Billie finished before Alex.Frankie finished before Drew.Alex finished before Drew.
Who finished where?
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.
?
Puzzle 144
Below is 88, moving only two lines, can you turn this into 81?
Note: this puzzle is not interactive, and cannot be clicked.
Hint
Which 2 lines are you moving, and where are they going?
Answer
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