Hummings of a Happy Hurkle

On Monday, you flip coins all day. You start flipping coins until you see the pattern Head, Tail, Head. Then you record the number of flips required, and start flipping again until you see that pattern, you record it, and start again. At the end of the day you average all of the numbers you’ve recorded.
On Tuesday you do the EXACT same thing except you flip until you see the pattern Head, Tail, Tail.

Will Monday’s number be higher than Tuesday’s, equal to Tuesday’s, or lower than Tuesday’s?

Solution over the fold.
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You didn’t really think one puzzle was the end of it, did you?

Fred and Norma held a dinner party and invited 4 other couples. As people arrived, Fred noticed that people who knew each other hugged or kissed, but if they were strangers they just shook hands. After all the arrivals and all the introductions, Fred asked everyone including Norma how many hands they had shaken. To his surprise he got 9 different answers.

How many of the dinner guests were strangers to Norma?

Answer over the fold (more…)

Time for another puzzle, to get the juices going again!

Instructions:

1. Deal out 2 full packs of cards in one long row, all face down (or in circles or loops or whatever, as long as you can count along them!).
2. Starting with the first card, turn over every card.
3. Starting with the second card, turn over every second card.
4. Starting with the third card, turn over every third card.
5. Starting with the fourth card, turn over every fourth card.
6. And so on, until every card has been used as a starting point.

Question: how many cards are now face up?
Bonus: what will be the effect of including the jokers?

Solution over the fold

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A mathematician goes into a restaurant and is seated at a square table, which he notices is unstable. The table has four legs evenly spaced, but although the floor is smooth he can see it is quite uneven. As a result one leg of the table does not quite reach the floor.

The waiter offers to wedge a piece of folded paper under the table leg, but the mathematician quickly analyses the problem and comes up with a better solution. Without getting up from his chair, he quickly moves the table so that it is now stable. Can you find how he did it?

The puzzle is to prove that there is a way to move the table to a nearby location so that all 4 legs rest evenly on the floor, and to find a simple method to do so.

You can assume that there are no holes, obstructions or other artificial restrictions. The solution should be perfectly practical under normal conditions, and may actually turn out to be rather useful!

Solution
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Alice, Bob, Carol and David are two parents and their son and daughter. The problem is to work out which is which.

You are told that:

* Bob and Alice are blood relatives.
* David is older than Bob.
* Carol is younger than David.
* Carol is older than Alice.

However, two of these statements are not true! Can you figure out this family?

Solution over the fold.
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Previous posts have given the rules for the puzzle and explained why traditional solutions fall down. The following is a complete solution. I suggest you don’t look until you have tried to solve the puzzle for yourself.
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There is a commonly given solution to this puzzle that depends on induction, but incorrectly in my view. Here’s why.

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The following logic puzzle is copied verbatim from a particular Web site. I haven’t given a link, and I suggest you give it a try before Googling.

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A horrible disease has broken out in the Kingdom of Faroffia. There is a wonder cure, and you have a 1000 bottles of it which must be distributed today to save the kingdom. Unfortunately, you have just found out that one of the bottles is contaminated with a deadly poison. You have a supply of laboratory mice which can be used to test for the poison, but because it takes some time to have its effect, you only have time to conduct one test.

How many mice do you need in order to find out which is the poisoned bottle?

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You are a young tech just hired by Artslet (your friendly Telco) and obviously someone is out to make your life hard!

You have just assisted your supervisor to lay 1 Km of special cable containing 100 individual wires. As he was about to head off for a very long lunch, he left you the job of tagging all the wires so they can be connected to the correct equipment, promising to buy you a drink if you get there before knock-off time.

Unfortunately, the wires are completely indistinguishable — this would have been a much easier job if you could have done it before the cable was laid!

To assist you in this task you have a large supply of numbered tags, a chart in which you have to record the tags attached to each end of each wire and a simple continuity tester consisting of a battery and a light. If you (say) joined 2 wires together at one end, you could then walk down the other end and test to find out which 2 wires are joined. There is no limit to how many wires you could join and test like this.

The question is: how far are you going to have to walk to tag and record all the wires? What strategy will you employ? Do you have any chance of the supervisor buying you that drink?

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