#29 How many strips?
How many 3 x 1 strips, like the example pictured, can be cut out of this piece of wood?
Answer next week
#28 A well-timed nap
Solution
One hour is 60 minutes for the minute hand, and 1 hour is one-twelfth of a circle (i.e. 30掳) for the hour hand. In other words, if the time is 鈥渕鈥� minutes past the hour, then the hour hand has travelled through 陆m degrees past the hour.
Suppose that when I go to sleep, the angle between the minute and hour hand = m. If the minute hand is ahead of the hour hand, this means (30 鈥� 陆m) = m. This is only true for m = 20, meaning the time is 3.20 pm. It is also possible that the minute hand is more than one hour segment ahead of the hour, i.e. 30 + (30 鈥� 陆m) = m, meaning m = 40, and the time is 6.40 pm.
If the minute hand were even further ahead, m = 60 + (30 鈥� 陆m) means m = 60, but we call 鈥�60 minutes past 9鈥� 10 o鈥檆lock. And if the minute hand isn鈥檛 ahead of the hour hand, then m = 陆m (midnight or midday, but neither can apply here) or m = (30 + 陆m) and all solutions are m = 60 again.
So I fell asleep at 3.20 pm and woke at 6.40 pm, having slept for 3 hours and 20 minutes.
Quick Quiz #28
1 Which chemical element is 鈥渕issing鈥� from the universe, with far less of it apparently about than the big bang theory says there should be?
2 The individual antennas of the Square Kilometre Array, planned to be the world鈥檚 largest radio telescope, will be built in Australia and South Africa. Where is the project鈥檚 headquarters?
3 In terms of cross-section, Hang So鈥檔 膼o貌ng near Vietnam鈥檚 border with Laos is the world鈥檚 largest what?
4 What are the longest and shortest bones in the human body?
5 Agreeableness, openness to experience, extroversion, conscientiousness and what other factor make up psychologists鈥� Big Five personality traits?
Answers below
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Quick Quiz #28
Answers
1 Lithium
2 Jodrell Bank Observatory in Cheshire, UK
3 Cave. It is some 200 metres high and 150 metres wide
4 The femur (thigh bone) and the stapes (stirrup) in the middle ear
5 Neuroticism