Barnaby’s Math

This is a direct transcript, found in the Williams family archives, apparently of a “Home Math Test” that Barnaby Williams took early on in his grade school career. The man asking questions on the recording is assumed to be Barnaby’s father, and Barnaby is providing all of the answers. While no records of Barnaby’s father remain, it’s possible, given the transcript that he was either a mathematician or some kind of baker.


Q: If four people are sharing 12 cupcakes, how many cupcakes does each have?

A: It depends on how they divide them up.

Q: They divide them up equally.

A: They each get three.

Q: Right. And how many cupcakes do these three people have?

A: Three

Q: No.

A: You just said that was right.

Q: Oh. Right, sorry, how many cupcakes do *all three* of them have *together*?

A: Nine

Q: Right. And how many are left.

A: Twelve

Q: No.

A: You didn’t say that anyone got rid of any cupcakes! I mean… did someone eat some of the cupcakes?

Q: No. Sorry, I meant that out of the twelve… I said that three guys had nine cupcakes…

A: *I* said that.

Q: Right, sorry. YOU said that those three guys had nine cupcakes and I’m saying how many are left if you don’t count those nine.

A: None.

Q: What about the last guy?

A: I thought you were talking about the three guys! If you don’t count the three guys and you’re talking about the three guys, then there are NO CUPCAKES! The three guys have nine cupcakes because they have three each, for some reason, and the last guy also has three because you said they had twelve!

Q: Okay! Right, no, clearly you actually understand all of this… You know what? Let’s switch this up. Let’s go to this other section. I give you two numbers and you tell me what the biggest number is you can make with them.

A: I love these, these are easy.

Q: Okay, four and three.

A: Seven.

Q: Okay, sorry, that was my fault. I give you two *digits* and you make the biggest number with them you can, right?

A: Okay.

Q: So if I give you four and three, you could either make forty three or thirty four, right?

A: Okay.

Q: Okay. Six and Two.

A: Just… like… Six six six six six six on and on forever, right?

Q: What?
A: Like infinity of sixes. I don’t even know why they have the two.

Q: …

A: What? Is that wrong?

Q: No. No, that’s totally… Okay… look at the example. You have to make the largest *two digit number* out of the two numbers I give you. So, if it’s six and two, there are only two numbers you can make out of it. Sixty two and twenty six.

A: Oh! Okay, you can only do… Okay, okay, okay. I can totally do this.

Q: Are you messing with me?

A: No!

Q: Didn’t you do this in school?

A: Yeah, but I didn’t, y’know… I didn’t *think* about it at school.

Q: Yeah, that makes sense. Okay, let’s try this again. Four and three.

A: Forty four.

Q: NO.

A: WHY? You said I had to make the biggest number possible using only these numbers and it had to be a two digit number!!!!

Q: You have to use BOTH NUMBERS!

A: WELL *NOW* you tell me! (laughs) You aren’t very good at instructions.

Q: Okay, look, let’s move on to the example, just do the chart on your homework. We’ll skip this – look, we’ll go to the last section, this is the three digit numbers.

A: Okay, I love this, it’s totally easy.

Q: Okay, you have to use all three numbers. It has to be a three digit number, and I want to know the largest number you can make and the smallest.


Q: So, you have to use the three numbers we pick from the number pile…


Q: And you have to make two different three digit numbers using all those numbers and never using one of them twice.

A: You’re trying to make this complicated but I KNOW YOU! You can’t trick me. I know how to do this ALREADY.

Q: Okay. Okay, good. Okay, I’m going to pick three numbers.

A: Let me pick them.

Q: (sigh) Okay, you pick them. (sound of numbers being picked) Okay, great. Two. Zero. Seven. Perfect.

A: I didn’t get my favorite number.

Q: What’s your favorite number?

A: Eleven.

Q: (…)

A: What?

Q: These are all – I mean, how are you gonna pick eleven?

A: If I pick One twice!

Q: Oh I see, now you have NO PROBLEM figuring out two digit numbers.
A: Oh! Did I get that one right!?

Q: Okay, let’s just do this. What’s the biggest number you can make with these three digits.

A: Seven… hundred and twenty?

Q: YES. YES. Exactly right, great job. And what’s the smallest?

A: Zero hundred and twenty seven?

Q: (…)

A: Isn’t that right?

Q: You know what? It’s exactly right. Should we go and watch a video?

A: Oh yes, definitely.