#22 The 9-minute egg
I like my eggs to be boiled for exactly 9 minutes. The problem is that I have no way to measure time except for two egg timers that are able to measure precisely 4 and 7 minutes respectively.
There is more than one way to set up the timers to measure exactly 9 minutes, but I am keen to eat my egg as soon as possible. Can you help?
Answer next week
#21 Six weeks of seconds
Solution
The number of seconds in six weeks and the product of all the whole numbers from 1 to 10 inclusively (10!) are the same: 3,628,800.
Here is how to show they are the same without a calculator:
The number of seconds in six weeks is
6 weeks × 7 days × 24 hours × 60 minutes × 60 seconds
Now, rewrite these numbers as products of smaller numbers.
For example: 24 = 3 × 8
60 = 5 × 4 × 3
which gives you:
6 × 7 × (3 × 8) × (5 × 4 × 3) × (5 × 2 × 3 × 2)
which equals:
6 × 7 × 3 × 8 × 5 × 4 × 3 × 5 × 2 × 3 × 2
Reorder and adjust this sequence, noticing that 10 = 5 × 2,
and 9 = 3 × 3
= (5×2) × (3×3) × 8 × 7 × 6 × 5 × 4 × 3 × 2
= 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2
= 10!
Quick quiz #21
1 In mathematics, the continuum hypothesis advanced by Georg Cantor in 1878 concerns the possible sizes of what quantity?
2 Pan troglodytes and Pan paniscus are the sole members of the Pan genus. How are they better known?
3 What is the main chemical component of standard glass?
4 John Bardeen, Walter Brattain and William Shockley shared the 1956 Nobel prize in physics for which discovery?
5 The hallux is the biggest of your whats?
Answers below
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Quick Quiz #21
Answers
1 Infinity. It states that while the infinity of real numbers (all numbers you can order along a line) is larger than the infinity of just the integer numbers, there is no level of infinity between the two
2 The chimpanzee and the bonobo
3 Silicon dioxide, SiO2
4 The electronic transistor
5 Toes