Thread: How Good Are You At Reasoning?

Here's some questions, some of which are quite cool, which you have to be quite mathematically minded to answer. I wanted to see how good people are at thinking rationally but creatively on DV. I threw in a couple of standard psychological experiments too. Just do the ones you can. Feel free to add more.


1. You have a row of 1,000 coins, all of which are heads up. You flip the second, fourth, sixth, and all other even coins over so that they're tails. Then you flip over the third, sixth, and all other coins which are multiples of three. Now you do this for every fourth coin, every fifth coin, etcetera, all the way up to every thousandth coin (which means just flipping the last one).

The question is this: which coins are heads up, and why? There is a concise and surprising answer.


2. What's the maximum number of pieces you can cut a pizza into using a cheese wire (i.e. straight cuts) if you can only cut six times? The pizza is to thin to cut horizontally, and too hot to pick up and move around.


3. There's a 1% chance that the average person has cancer. Somebody with cancer has an 80% chance of testing positive when they go for a scan. Somebody without cancer has a 9.6% chance of testing positive (i.e. getting a false positive). You go for a scan and receive a positive result. What is the probability that you have cancer?


4. 100 people out of a group of 10,000 are tree-huggers. You ask all 10,000 people if they hug trees or not. 80 out of the 100 people who hug trees are honest about it and say yes. 950 out of 9,900 people who don't hug trees also pretend that they do. What fraction of people who claim to hug trees are genuine tree-huggers?


5. I have four cards with numbers on one side and colours on the other. I claim that cards with even numbers are red on the other side. I put the cards in front of you. They are

1, 2, red, blue.

Which cards do you need to turn over to check my claim?


6. In the UK you can drink at 18. There are four people drinking at the bar. One is 21, one is 16, one is drinking coke, one is drinking beer. What do I have to check to make sure nobody is breaking the law?


7. In any group of (two or more) people, there are always at least two people with the same number of friends in that group. True or false?

N.B. you can only be friends with somebody who is friends with you!