# Math with dinosaurs

Doctor Brun was at it for years, but he'd finally got his time machine up and running. His first trip was to a time way back in the past when dinosaurs roamed the Earth. To his surprise, the dinosaurs were actually quite intelligent. His first encounter was with Timmy Rex (a Tyrannosaurus Rex). They began talking about philosophy and politics. Eventually, mathematics came up. Here's the part of the conversation they had, including some of the cave writings.

Doc Brun: Ok. Just to be sure we understand each other, can you complete these equations for me?

Doc Brun wrote $1 + 2 =$

T. Rex wrote $3$

Doc Brun: Great. And this one?

Doc Brun wrote $12 \times 3 =$

T. Rex wrote $102$

Doc Brun: What? That's not right at all. Let's try another. I think I see what's going on here. Is this equation right?

Doc Brun wrote $1 + 3 = 4$

T. Rex: I don't even understand what you wrote there!

Doc Brun: I see, just as I thought. I'm assuming that--

The frustrated T. Rex hastily ate Doc Brun in one bite.

What was Doc Brun going to say before he was swallowed?

• this was an easy one, but the prompt was top drawer! +1 – DLeh Feb 12 '15 at 16:45
• @DLeh Thanks. I thought that it might be easy to find out what was happening, but the interesting part to me is why (see the end of KSmarts' answer). – blakeoft Feb 12 '15 at 17:45

It appears that the dinosaurs do mathematics in base $4$.

If this is the case, when Doc. Brun writes $12\times3$ he expects the answer $36$, which T. Rex writes as $210$, in base $4$. However, T. Rex should read this as $6\times3$, since $12_4=6$, so he would give the answer $18$, which is $102$ in base $4$.

Base $4$ would only contain the digits $0$ through $3$, so T. Rex would not recognize the glyph "$4$".

This also makes sense because a Tyrannosaurus Rex only has two fingers on each hand, for a total of four fingers. The main reason that humans started using base ten is because it is easy to count to ten—just count on your fingers! So T-rex math would likely use base four.

First I thought, that the dinos used a numbering system, based on 4.

1 + 2 = 3 would fit here, but 12 * 3 = 210 would be 6 * 3 = 18 in decimal system. 210 in decimal is 36. Am I missing a 2? Or It should be 102...

• Yes, $12_4 \times 3_4 = 6 \times 3 = 18 = 102_4$. This has since been fixed in the question. – Ionoclast Brigham Feb 12 '15 at 5:10

The dinosaurs were doing mathematics in base 4.
Then numbers 1, 2, 3, 12, and 102 in dino language mean
the numbers 1, 2, 3, 6, and 18 in our decimal system.

T. Rex does not understand 1+3=4, as the digit 4 is not used by the dinos.

• Does this add anything to the earlier answers by KSmarts and buffo? Maybe it should be deleted? – Rand al'Thor Mar 16 '15 at 16:14