#219 The second red queen
Set by Rob Eastaway
鈥淵ou know that debt you owe me?鈥� says Svengali, rather menacingly. 鈥淚 am prepared to write it off 鈥� but only if you have a bit of luck.鈥�
He takes out a regular pack of playing cards and gives them a thorough shuffle. 鈥淣ow,鈥� he declares, 鈥淚 am about to turn over all the cards one at a time, but first I want you to predict the position of the second red queen that I will turn over. If your guess is correct, I will write off your debt.鈥�
My odds aren鈥檛 high. There are 52 cards in a pack. Only two of them are red queens 鈥� the queen of hearts and the queen of diamonds. And only one of those will be the second red queen to be turned over.
鈥淚 will give you one bit of advice,鈥� says Svengali, noting my pensiveness. 鈥淒on鈥檛 choose the top card, because by definition that cannot be the second red queen 鈥� though it might be the first.鈥�
Which card position in the range 2 to 52 should I nominate for the second red queen? Or should I just pick a random number?
Solution next week
#218 Playground parity
Solution
The total number of children must always be a multiple of 12.
In the original situation, we can say there were X children in one group (swings) and Y in the other (climbing frame). We know X + 2 = 2(Y 鈥� 2) and that X 鈥� 2= Y + 2. Solving these simultaneous equations reveals that X was 14 and Y was 10, making 24 children in total.
If N children swap from one group to the other then X + N = 2(Y 鈥� N) and X 鈥� N = Y + N, which leads to X = 7N and Y = 5N. This makes the total number of children 12N.
Quick quiz #199
set by Bethan Ackerley
1 An animal with the same name for both its genus and species, such as the red fox (Vulpes vulpes), is known as what?
2 What was the most powerful nuclear weapon ever tested by the US?
3 Where in the body would you find a Baker's cyst, also known as a popliteal cyst?
4 The comet Tempel 1 was visited by which NASA probe in 2005?
5 What is the most abundant gas in Earth's atmosphere?
Quick quiz #199
Answers
1 A tautonym
2 Castle Bravo, which had a 15-megaton yield
3 The back of the knee
4 Deep Impact
5 Nitrogen