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P P P U U Z Z Z Z Z L L L L E S S gives 3 x P, 2 x U, 5 x Z, 4 x Z (only 4 as we've already used one), 4 x L, 1 x E, 2 x S.
3 * 2 * 5 * 4 * 4 * 1 * 2 = 960.
Puzzle 1239
Traffic was bad going to work this morning. I only managed to average 30 mph.
How fast must I go home tonight, along the same route, to average 60 mph for the entire round trip?
[Ref: ZNID]
Hint: It doesn't matter what the distance is, so try a random distance.
Answer: This cannot be done.
It does not matter how far the trip is, let's assume that it is random distance, say 60 miles, and remembering that Time = Distance ÷ Speed.
The morning trip took 60 miles ÷ 30 mph = 2 hours.
To average the required 60 mph, we would have to travel the total distance (of 120 miles) in 2 hours. However, we've already used all of the two hours for the morning trip!
Choosing any random distance would also show that it can't be done.
Puzzle 1240
My bath has two taps and a plug hole.
The cold tap on its own fills the bath in 12 minutes, the hot one in 5 minutes.
The plug hole can drain the bath in 30 minutes with the taps off.
How long will the bath take to fill if I leave both taps on with the plug left out?
In 1 hour, the cold tap could fill 5 baths, the hot tap could fill 12 baths and the plug could drain 2 baths.
Therefore, in 1 hour, we have 5 + 12  2 baths full = 15 baths.
Therefore each bath would take 4 minutes to fill.
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