think again!

If four empty milk bottles can be exchanged for one full milk bottle, how much milk can I drink if I have 24 empty milk bottles?

- Do you like my three digit number?
- Not too bad, but look at this!
- What?
- When I multiply the three digits the result is 1/5 of the original number.
- That is strange!
- I agree. I thought it would be bigger.

- How was the party?
- Great! You should have been there!
- Did many show up?
- That was one of the curious things.
- What was?
- We discovered that three of the people had birthday in the same month and on the same day of the week.
- So what?
- After having partied for a while my girl friend discovered that it was no coincidence.
- What was no coincidence?
- She demonstrated that we were the minimum number of people for that to happen.
- For what to happen?
- We were the minimum number of people so that one would be certain that three of us were born in the same month on the same day of the week.
- Maybe I didn’t miss a lot after all.

- How is your new house going?
- Don’t talk about!
- What’s up?
- Right now they are making the steps to the bedrooms upstairs.
- And?
- The stairs elevates the climber 3 metres. How high should each step be? How wide should each step me? How much space will the stairway take?
- Are you asking me?
- No, I am ordering fries.

- I have an unlimited supply of 3×3 and 7×7 squares.
- I have always envied you that!
- The squares?
- No, what you do with them.
- What do I do with them?
- You tile them to together to make bigger squares.
- How did you know?
- I can see it in the way you walk.
- Is it that obvious?
- Out with it, what is the problem?
- With my 3 and 7 squares I can only make some bigger squares. Which? What do they have in common?
- Is that all?
- My wife has squares of side 2, 7, and 11. What is the smallest square these can tile if its side is not a multiple of 2, 7, or 11?
- You ask me?
- No, my wife asks me.
- Why did you marry her?

When I weighed the kitten above I used a pan balance. I remember that the kitten weighed 2009 grams. I had an unlimited supply of 1 gram weights, 10 gram weights, 100 gram weights, and 1000 gram weights. What I don’t remember is in how many ways I selected the weights to balance the kitten. I tried every possibility, but I don’t remember how many there were.

Problem source: Mathematical problems, University of British Columbia.

- Ten pennies are placed in a circle.
- I am not blind.
- They are all showing Heads.
- I see.
- Can you make them all show Tails?
- No problem! Just turn them over.
- You can only turn three adjacent coins at a time.
- Then I don’t know if it is possible.
- If it is, find the least number of moves needed.
- Can I try to solve the problem with five pennies first?
- I did not know you were cheap, but be my guest.

Problem source: Wisconsin mathematics, engineering and science talent search.

- Do you see this cable?
- That’s a very long cable if ever there was one!
- The cable has one thousand wires in it. I would like to know which wire at this end corresponds to which wire at the other end.
- Seems like a reasonable request.
- I have a battery and a light bulb to help me.
- No wonder I could not find them this morning!
- The bulb will lit up if I make a closed circuit with the wires.
- Can you connect the wires at each end?
- Yes, as much as I please.
- Let’s get to work then.
- Not so fast. I want to minimise the number of times I have to go from one end of the cable to the other.
- Can you see if the bulb is lit from the other end of the cable?
- Sure can.
- Are the wires coloured?
- Unfortunately no.
- I think I know the solution if there are two wires!
- There are one thousand wires.
- Just making conversation.

Problem source: wu:riddles.

- This is from a game I played las night against Celia.
- Who won?
- Can you find out what the last move was in the position in the diagram?
- Whose turn is it?
- That is a good question.
- Either Black moved the king or White moved the knight or the king.
- That’s a good start!

Problem source: Rund um das Schachbrett by Karl Fabel.