Magnus Carlsen, the no 1 ranked chess player, challenges you here. Solve three puzzles in record time and be no 1 on his list.
By the way, the world’s no 1 is now playing in the Tata Steel tournament. Read about it in his blog, or follow it on the official web site or watch the games commented at chessbomb.
Oh, I almost forgot, how did you do in the challenge? Me?! Number 354 on the list with no improvement in sight.
- Nice to see you home again!
- Thank you.
- It must have been quite an ordeal!
- The food was good.
- OK. But you were arrested unlawfully?
- It made me think.
- I am glad you see the positive in every situation.
- I mean, I had to think hard to be released.
- How come?
- Just after my arrest I was given 100 coins and I was asked to divide them into two piles with 25 magic coins in each.
- Magic coins?
- I was told 50 of the coins were magic, but I could not see which.
- So how could you do the task?
- I found a way that guaranteed success in 50 or less tries.
- Amazing!
- I agree.
- Now that you are a free woman again, what are your plans?
- I am building prisons.
- What?
- My plan is to arrest politicians and release them when they have demonstrated some thinking skills.
- Interesting! Which skills do you have in mind?
- Any.
Problems source: The Emissary Newsletter’s Puzzle section by Elwyn Berlekamp and Joe P Buhler.
- How old are you?
- 67.
- That is a lot!
- Thank you!
- What is 67 in base 2?
- Let me get out my wallet and see.
- Why your wallet?
- My memory is fading.
- So what?
- I have it written down on a piece of paper that I keep in my wallet.
- Sorry for asking!
- 67 is 1000011 in base 2.
- Now put some + signs between the digits.
- How many?
- As many as you like, but not more than one + sign between two digits.
- Will 100 + 0 + 1 + 1 do?
- Excellent! How much is the sum?
- 6.
- What is 6 in base 2?
- 110.
- Now repeat the process. Add + signs at will.
- 1 + 1 + 0.
- How much is that?
- 2.
- Repeat the process.
- 10 is 2 in base 2. 1 + 0 = 1.
- That’s it?
- What’s what?
- You can stop.
- My time is up?
- You reached 1.
- That is the aim of this game?
- Oh, I forgot to say so?
- No harm done.
- Well, yes. The question is if any positive number can be reduced to 1 in this way?
- Who want’s to know?
- The tomato farmers of Italy.
- Really?
- Yesterday I got an email from the World Processing Tomato Council (WPTC) asking for help.
- What have you found out?
- I believe it can always be done. Even more, I think it always can be done in n steps or less.
- What is n?
- It is whispered in high circles that n ”is a real shocker.”
Problems source: The Emissary Newsletter’s Puzzle section by Elwyn Berlekamp and Joe P Buhler.
(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.