thnik again!

(Illustration taken from Wikipedia.)

- Did you know that Tartaglia’s triangle is also called Pascal’s triangle?
- I had no idea.
- Did they both invent it?
- Neither of them did.
- I see.
- Can you find a row in the triangle with four different numbers in it?
- 1 4 6 4 1 should do.
- Are two of the numbers twice the other two?
- No, I am afraid not.
- Can you find a row where they are?
- Is this a hard problem? I am rather busy doing nothing these days.
- Can you prove that there are infinitely many such rows?
- Then finding one can’t be that hard.
- Interesting thought!

Problems source:  The Emissary Newsletter’s Puzzle section by Elwyn Berlekamp and Joe P Buhler.

- How did the party go?
- Which party?
- The Communist party.
- The Communist party?
- No, silly! I am joking. The birthday party yesterday.
- Oh, that! Not too well. If you don’t mind, don’t let’s talk about it.
- Why not?
- Well, if you have to know.
- I have to. I am writing this blog called Thnik again!
- Couldn’t you at least get the spelling wright?
- Tell me about the party. There were five kids, right?
- 5 kids and 3 identical cakes.
- The cakes were the problem? Too much flour?
- The kids wanted the same amount of cake.
- So you divided each cake in five and gave them three pieces each?
- I wanted to, but the kids wanted bigger pieces.
- What do you mean? Did you have more cakes?
- They wanted the smallest piece to be as big as possible.
- Did you find a better solution than what I just suggested?
- I’d rather not talk about it.

Problems source:  The Emissary Newsletter’s Puzzle section by Elwyn Berlekamp and Joe P Buhler.

- A friend of mine has 25 horses.
- So he has to buy his milk?!
- He wants me to determine the three fastest and the order of them.
- But that is impossible! They will run fast one one day and not so fast the next.
- Not these horses. They always run at the same speed.
- But what if some of them run at the same speed?
- They don’t.
- Some kind of horses! Maybe he doesn’t have to buy his milk after all.
- I can pick any five of the horses and let them race. My friend will tell me the order they finish in, but not the time they take.
- How many races can you do?
- That is the problem. He wants me to determine the best, second to best, and third to best horse with as few races as possible.
- I have an innocent question. This is what they call applied maths?

Problems source:  The Emissary Newsletter’s Puzzle section by Elwyn Berlekamp and Joe P Buhler.

- I can tell how old you are.
- No, you can’t.
- How many times will 10 go into your age?
- I won’t tell you!
- No problem. Take the number and multiply it by 5.
- OK.
- Add 3.
- OK.
- Double it.
- OK.
- Add the last digit of your age to the result of the addition.
- OK.
- Subtract 6.
- OK.
- What number do you have now?
- My age!
- What is it?
- I told you: I won’t tell you.

When I was a kid, 13, I was amazed by ‘tricks’ like these. Find some kids and watch their reaction. Are they amazed, bewildered, or bored? Can they explain how the trick works?

Problem source: http://www.mathconcentration.com/

- For Christmas I got a pool table.
- Really?! Does it fit in your apartment?
- It is just a miniature version. It fits on the dining table.
- I see.
- I have been losing constantly to my young son.
- I am not surprised.
- The 15 balls are numbered 1-15. The first one to pocket a ball will try to pocket balls of the same parity.
- Translation please!
- If I pocket 4 I will get the even balls, but if I first pocket 11 I will get the odd balls.
- What about ball 8?
- When someone has pocketed all his ball he has to pocket the 8 ball to win.
- I see.
- It is a nice game!
- Now I know why you may have lost a lot.
- But you haven’t even seen me play!

- I am thinking of a number.
- Any number?
- It is prime.
- I was once in my prime.
- It is the smallest prime number that is equal to the sum of two prime numbers
and is also equal to the sum of three different prime numbers.
- Really?! It is the same as my house number!

A two-digit number is seven times greater than the sum of its digits.

“Around 20 years ago, a scientist named Scott Feld was looking at a survey of teenagers and their friends. He looked at the total number of friends one student had, and then looked at the average number of friendships those friends had. After repeating this experiment over and over, he came to a startling conclusion. For most people, their friends were more popular, on average, than they were. He puzzled over the result, and then came up with a very neat explanation.”

Please, do the same!

Source: maths + stats by email by http://www.csiro.au.

In which region of the table may I put ball B so it can be hit by ball A when it rebounds from the upper and right side?

Problem source: Estímulo del Talento Matemático.

- I want to shoot the billiard ball A so it hits B.
- That shouldn’t be too difficult.
- A has to rebound from two of the sides before it touches B.
- What is the shortest route?
- Exactly!

Problem source: Estímulo del Talento Matemático.