#04 Which Door?
You may have heard of the US game show Let鈥檚 Make a Deal, in which the star prize is hidden behind one of three doors and the contestant has to pick the lucky door.
Now there is a new game show, Let鈥檚 Make a Bigger Deal, hosted by Jayne Brody. There are five doors, A, B, C, D and E, and contestant Nico is allowed to choose three. If the prize is behind one of them, he wins. Nico picks doors A, B and D.
As always happens on the show, to build drama, Brody opens three doors (two of them Nico鈥檚) that she knows don鈥檛 have the prize behind them: A, D and E. Two remain closed: Nico鈥檚 (B) and C. Brody says: 鈥淣ico, do you want to stick with B, or switch to C? You can phone a friend if you want.鈥�
Nico likes this idea and rings his friend Leah. 鈥淗i Leah, there are two doors left. Should I choose door B or door C?鈥� Which should Leah suggest? And should Nico follow Leah鈥檚 advice?
Answer next week
#03 Cube shadow Solution
The largest shadow that a cube can cast is the shape of a hexagon: the cross-sectional shape you get when you point one corner of the cube at the sun.
If the cube鈥檚 sides are 1-metre long, the area of a square face is 1 square metre. The triangle ABC in the diagram has sides of length 鈭�2 since the line AB is a true view of the cube face diagonal. The area of equilateral triangle ABC is 鈭�3/2.
The total area of the hexagon is twice this (made up of six triangles identical to ABD). Hence the total area of the shadow is 鈭�3, roughly 1.73 m2.
Quick quiz #04
This time with a twist鈥�
1 Which dinner plate delicacy has the formal taxonomic name Solea solea?
2 Which thermodynamic-sounding measure of information complexity is named after the US 鈥渇ather of information theory鈥�, who died in 2001?
3 Buckingham Palace, St Paul鈥檚 Cathedral and the Bank of England are among London landmarks built using which grey-white Jurassic limestone?
4 On 20 July 1976, which NASA probe made the first fully successful soft landing on Mars?
5 Which meteorologist and naval officer was captain of Darwin鈥檚 Beagle?
Answers below
Bonus question What connects all five answers? (answer next week)
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Quick quiz #04
Answers
1 Common or Dover sole
2 Shannon entropy, after Claude Shannon
3 Portland stone
4 Viking 1
5 Robert FitzRoy