Mastermind

Hello mathematicians!

Hi everybody.

Hi Barbara!

Hi Michelle.

Are you ready?

I am.

Okay, so we're gonna play a game today called Mastermind.

Oh sounds like me.

I think it sounds like me, but let's play. So we each have a square of paper. Can you show your square? And on our square of paper we need to write a three-digit number.

Okay.

But none of the digits can repeat.

Okay sounds good.

So you write yours and I'll write mine, don't show me.

Okay.

Okay everybody here's my number. [462] Okay and Barbara can you show everybody your number.

Here's my number there [305].

Okay, so now what we need to do is, we're gonna make up our game board, and so on it we want to record what the guess was. I'm gonna have 3 columns. In here we want to know, um, how many places, and how many digits.

Okay, what does that mean?

So you know how we just wrote a three digit number?

Yep.

So I might say to you, hey Barbara, was the number 426. Mm-hm and I would write 426 and then I'd say to you, oh we should have actually written that the other way around, digits.

Okay.

And places.

Okay.

Cuz then you would say to me there's one digit or three digits or two digits that, or no digits.

That are correct? Okay.

And then you would say to me, it's in, there's one of them is in the right place.

Okay, so places means in the right spot and digits means the digit is in the number.

That's right. Okay so let's play because that's the easiest way I always find to learn.

Yeah me too!

So how could we decide who goes first but what about the person with the longest, the most letters in their first name.

Okay I think I've got you because Barbara's got some extra letters in there. B. A, R, A so 7.

Well but Michelle has 8.

Oh no!

Thanks to the French. All right so, I'm gonna try to guess what your number is. Um, what about 753. 753, okay, you've got one number correct.

Do you mean one digit?

Sorry, one digit correct.

One digit correct, mm-hmm. And, but, it's, it's not, none are in the right place. It's not in the right place, so I'm writing one digit is in the number and none of them are in the right place.

That's right.

Okay, so it's your turn to guess.

Okay, so 624.

Okay so I'm gonna show the guys at home. [462] Mm-hmm, so I'm gonna say to you that three digits are correct.

Oh okay!

And none of them are in the right place.

Okay, that's kind of useful because it means I've got to change everything.

Uh-huh.

Okay, so now what I'm thinking about is, I know one of these is correct, so I'm gonna have to take a guess but I'm gonna use one of them again, but in a different place. So I might say, for example, keep the three, and say, 300 and something.

Okay.

Right, because, or I could say 500, but I wouldn't say 700 and something again, cuz you told me that one of the digits is correct, but it's not in the right place.

That's right, yeah.

So I might say, 302.

Oh, Michelle I made a mistake, you actually had two digits in the, you had two digits correct. Okay, but still none of them are in the right place.

Oh okay.

That changes things a little bit, I'll just remind everyone what the number was [305].

Well I'm gonna keep 300 cuz I wrote it.

Okay.

Um but I wouldn't say 350 something.

No because..

Because that'd be there.

Yeah, so I might say 370.

So 370? Okay, so you've got two digits correct.

Okay.

And you've got one in the right place.

Okay.

Okay, so now I've got to change everything around. So I'm gonna say 462.

3 digits correct, 3 digits in the right place.

Oh brilliant!

Oh fantastic. Yes!

Do you wanna keep going with mine? Yeah because something really interesting is happening, that I want to see how you go.

Okay, so, so what I don't know, I'm not sure whether it's the 7 or the zero is right. Mm-hmm but I'm, but but, and I'm not sure if the three is in the right place, or the 7 is in the right place. So I have to like, keep reasoning through, right, so I'm gonna hold this, this I'm gonna hold the 3 here, and then to test it I might say 307.

Okay, so in 307.

Do you want to show those guys. Yep here you go [305]. You've got 2 digits correct. Uh-huh. And 2 digits are in the right place.

Oh okay, so now what I am thinking, is that, I'm pretty confident the 3 is okay. Mm-hmm. I think the zero is okay, but it's not 7.

Okay, so if it's not, okay, I shouldn't give you any clues, but if it's not 7 what could it be?

Well I'm actually wondering if it, I am wondering, still about this 5, as well. Because I guessed it was 7 but I could, it could still also be the 5, because I haven't checked, tested that. Yeah. So what I might do is now just test 305 to see whether it's the 7 or the 5 that I was guessing here, to confirm my thinking.

Okay.

So, and that will also then tell me if the 3 and the zero are in the right place and I'll have confirmation.

Are you ready?

Yeah.

3 digits correct.

Yes!

And how many do you think are in the right place knowing what you've seen?

Well now 3.

You're correct.

Yes!

Well done!

Cool. I got really excited because, it looked like you were giving up on the 5 but then as you gave up, it looked like you were giving up on the 5, but you introduced the zero, which was in, which was actually part of my number, so that's why I wanted, even though I beat you and I like beating you. I really wanted to see you work it out.

Because you also sort of, not to take away from your win, because it was. It was a bit lucky.

It was lucky. It was a bit lucky, the first part was lucky, and then that was the first time I just thought, I'll just put the yeah four in the hundreds. Yeah, I'll make it 462 but that, I got quite lucky, whereas you had to reason. I had to reason through a bit more.

Anyway, mathematicians we hope you really liked this game Mastermind. You could play it with four digit numbers, with two digit numbers.

Can you play where you repeat the digit or is that does that make it a bit? Have a go and see what happens! Okay. Have fun!