Archive for the ‘Problem’ Category

Got milk?

Tuesday, June 30th, 2009

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?

That is strange!

Monday, June 29th, 2009

- 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?

Friday, June 26th, 2009

- 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.

Some numbers are more famous than others

Thursday, June 25th, 2009
Find the smallest integer that can be written as the sum of two cubes in exactly two different ways. Why is it famous?

Fries with that?

Wednesday, June 24th, 2009

- 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.

Marital problem

Tuesday, June 23rd, 2009

- 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?

Misleading picture

Monday, June 22nd, 2009

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

Friday, June 19th, 2009

- 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.

Not exactly wireless

Thursday, June 18th, 2009

- 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.

Whatever happened?

Wednesday, June 17th, 2009

- 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.