More or Less Christmas quiz 2008

More or Less Christmas Quiz 2008

These are the quiz questions presenter Tim Harford used to test the numerical nous of comedian Dave Gorman and TV presenter Konnie Huq in BBC Radio 4's More or Less Boxing Day programme. Think you can do better? Then have a go.

Breeding boys

A country is preparing for a possible future war. Its tradition is to send only men into battle, so they want to increase the proportion of males to females in the population. A law is passed which requires every married couple to have children and to continue to do so until they have a boy.

1.) Multiple Choice Question

What effect do you expect this law to have on the population?

1. More boys will be born
   
2. More girls will be born
   
3. There will be no change to the gender balance
   

River Crossing

A farmer is taking a wolf, a goat and a basket of cabbages to market. He reaches a river where there is a small boat - only big enough for him and one other thing. He can't leave the wolf with the goat as it will eat it, or the goat with the cabbages as it will eat them. Fortunately the wolf detests cabbage.

2.) Multiple Choice Question

What is the least number of crossings the farmer can do?

1. 5
   
2. 7
   
3. 6
   

Magic show

A magician pulls out an ordinary deck of playing cards and gives it to a member of the audience to shuffle. The deck of cards is then put inside an empty box. The magician asks another audience member to name a card. They say, "Ace of Hearts".

3.) Multiple Choice Question

What is the probability that the magician then pulls the Ace of Hearts out of the box?

1. 1 in 52
   
2. 100%
   
3. None of the above.
   

Health screening

Imagine there is a condition in the population that affects one in 1000 people. A test is developed which is 95% accurate - it gives false positives in 5% of cases and it doesn't give any false negatives. You take the test and it tells you that you have the condition.

4.) Multiple Choice Question

How likely is it that you actually do have the illness?

1. 95%
   
2. 100%
   
3. 2%
   

5.) Ancient numbering: Babylon

What sort of numbering system did the Babylonians use?

1. Base 60
   
2. Base 12
   
3. They were the first civilization to use base 10.
   

6.) Ancient numbering: Roman

Multiply the following Roman numerals: XII by XII. Which is the correct answer?

1. MXLIV
   
2. CXLIV
   
3. VILXC
   

Bonus question (not included in the radio show)

An architect tells you his latest skyscraper is designed to last 60 years. He says it is built to survive extreme weather events. Only the sort of wind speed experienced on average once in every 100 years could topple it.

7.) Multiple Choice Question

What is the probability that the building will be blown down during the 60 years it is designed to last?

1. 1%
   
2. 45%
   
3. 60%
   

Answers

1. The country's leaders will be frustrated to find there is no change to the gender balance. Whoever has the children, the chance of a boy is always 50/50. If people keep having children until they have a boy, the number of males in the population might increase - but not the proportion.
2. The farmer would have to cross the river at least seven times. First of all, he would take the goat. Then he would return to collect the cabbages. He would bring the goat back with him when he returned for the wolf. He would then take the wolf across to sit with the cabbages, while he went back to fetch the goat. Exhausting!
3. There is no easily-calculated answer to this question because you don't know all the facts. It is unlikely to be 1 in 52 because magicians don't tend to get their tricks wrong. But you can't say it's 100% either: perhaps the magician deliberately fails to pull out the right card in order to make a later feat more impressive (such as the Ace of Hearts being found inside someone's pocket). Or perhaps the magician is Tommy Cooper.
4. If you did the test on 1000 people, one person would probably have the condition, while 50 would be false positives. One out of 50 is 2%.
5. They used a base 60 or "sexagesimal" system.
6. XII represents 12. Multiplying 12 by 12 gives 144 - or CXLIV, because C is 100, XL is 40 and IV is 4.
7. Worryingly, there is a 45% chance it would be blown down. The way you calculate this is too tricky to explain here - so you will just have to trust us on this one!

Your Score

0 - 2 : Must try harder

3 - 5 : Good

6 - 7 : Excellent!