Puzzle 473
At the local racetrack, Alex was testing the latest car.
During the eight test laps, Alex managed to average the first two laps at 100mph, the next two laps at 102mph, the next two laps at 140mph, and the last two laps at 150mph.
What was the average speed for the entire 8 laps?
Puzzle Copyright © Kevin Stone
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Hint
Remember that Time = Distance ÷ Speed, and try setting the track length to be a random length.
Answer
119mph.
Reasoning
It doesn't matter how long a lap is, so let's set the track length to be a random number, say 5 miles.
Using:
Time = Distance ÷ Speed
The first two laps took:
10/100 hours
The second two laps took:
10/102 hours
The next two laps took:
10/140 hours
The final two laps took:
10/150 hours
Therefore, the total time for the 8 laps was:
10/100 + 10/102 + 10/140 + 10/150 hours
The 8 laps were 40 miles, and using Speed = Distance ÷ Time:
average speed = 40 ÷ (10/100 + 10/102 + 10/140 + 10/150)
= 119 mph
Puzzle 474
A farmer buys chicken feed for 47c per tonne, pig feed for $1.23 per tonne and cattle feed for $1.44 per tonne. The feed can only be purchased by the tonne, and part tonnes aren't sold.
How much of each would they have if they bought 100 tonnes for $100?
Puzzle Copyright © Kevin Stone
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Hint
One of the answers is 28 tonnes.
Answer
38 tonnes of chicken feed, 34 tonnes of pig feed and 28 tonnes of cattle feed.
Puzzle 475
What letter is missing from this sequence:
A A A A {?} A A A A A A
Clue: the answer is not A!
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Hint
Think of an alternative alphabet.
Answer
N.
From epsiloN, last letters of the Greek alphabet, alpha, beta, gamma, delta, epsilon, zeta, eta, theta, iota, kappa, lambda, mu.
Puzzle 476
How many people must be at a party before you are likely to have two having the same birthday (but not necessarily the same year)?
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Answer
23.
Reasoning
By likely, we mean greater than 50% chance.
With one person there is a 0 percent chance that you'll have two people with the same birthday.
With two people the probability that they won't share a birthday is 364 / 365. The probability that they will share a birthday is therefore 1 - (364 / 365).
With three people the probability that they won't share a birthday is the same as for two people, times 363 / 365. So the probability that three people will share a birthday is 1 - (364 / 365) x (363 / 365).
Notice that with each additional person added, the probability that they shares a birthday with one of the previous persons goes up, because there are fewer "free" days remaining.
We keep adding people until the %age is greater than 50%.
When we have 23 people the %age is 50.729%.
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