The Binary Dino Puzzle
A nerdtastic adventure with children’s toys and binary
On my daughter’s 1st birthday she got a cute dinosaur that ate circular discs with different fruit printed on them and sang a song for each one. Someone asked, “how does it know one piece of plastic from another?” and that question secretly sent me into a nerd adventure.
This is the story of the Binary Dino; “my daughter’s toy” and a fun puzzle.
![](https://miro.medium.com/v2/resize:fit:700/1*3R6U1xeB7CGSIKMchNw8UA.jpeg)
You feed the Dino a mushroom 🍄, it knows. You feed the Dino apples 🍎, it knows. My first thought is that each plastic disc has some kind of RFID token, and the head had some kind of low power RFID reader. Yeah… in a children’s toy? C’MON GANT!
Here’s the Dino in action. Listen to its response after each disc:
An RFID reader would be a bit excessive for a children’s toy. Upon closer inspection, the Dino’s mouth had 4 taste buds.
OK… OK, 4 momentary switches, but I like thinking of them as taste buds. As each circular disc gets pressed into the mouth, it makes sense that the sides of each disc would activate some unique combination of these switches.
![](https://miro.medium.com/v2/resize:fit:700/1*2M1JwaZoX7JdWMqa5OZqXQ.jpeg)
Each switch is either pressed (on) or bypassed (off), just like bits in a computer. So, BINARY!
If you’re familiar with binary, you know 4 bits provide 16 possible permutations (0000 to 1111).
Nerd out moment! Binary is magical like that, since it’s the smallest super-increasing set, the max value 1111 (15) also represents the number of possible permutations sans zero.
That is 2^x -1= binary 1, x times
By pressing unique combinations on these “taste-buds” we can fire a unique response in our Dino.
We’ll throw out all-zero (0000) since that’s the default state (off/ready). So that leaves us with 15 possible flavor combinations, right?
Let’s take a look at the discs to see if we’re right!
The Discs
The toy comes with 8 discs, not 15. But we are right about the unique edges. I stacked the discs into a single column and quickly converted the higher ridges to 1s and the lower ridges to 0s. I then converted that binary to base 10 and surprisingly the numbers jumped around a bit.
![](https://miro.medium.com/v2/resize:fit:700/1*BsmBCiApzgnR1Q8mOuba9g.jpeg)
I’ll admit, I had no clue what was going on at first. The numbers don’t fit any pattern I would expect, they don’t even fit any well-known sequence I could think of! Why skip 4? Why skip any numbers? Fun Fact: 1, 2, 3, 5, 6, 7 is how you count your steps if you’re Salsa dancing, but that has nothing to do with this, right? If I hold down the pins for missing discs will I break my kid’s toy? Will it go into developer mode? Will it speak Piglatin?
Perplexed, life moved on, and I finally gave the toy back to my daughter with a few unanswered questions. Randomly, later, it hit me. I figured it out.
OK, so take a minute and pause. As of this moment, you have all the info needed to figure out this puzzle of the strange numbers.
1, 2, 3, 5, 6, 7, 9, 11
Ready?
Why those numbers? Why don’t we have more flavors? What will happen if we set the pins for 4, 10, or 13?
The answer comes when you stop thinking in base 10, and you think like a child. Adults feed the discs with the picture of the food on the top, but any kid would feed a circular disc however it fits. That means every circular disc could be fed upside-down. Could it be that simple? The skips are upside down repeats? Let’s check!
I’m going to list out the values/binaries and bold only the disc values:
Value 1 — Binary 0001
Value 2 — Binary 0010
Value 3 — Binary 0011
Value 4 — Binary 0100 ➡ Upside down 2
Value 5 — Binary 0101
Value 6 — Binary 0110
Value 7 — Binary 0111
Value 8 — Binary 1000 ➡ Upside down 1
Value 9 — Binary 1001
Value 10 — Binary 1010 ➡ Upside down 5
Value 11 — Binary 1011
Value 12 — Binary 1100 ➡ Upside down 3
Value 13 — Binary 1101 ➡ Upside down 11
Value 14 — Binary 1110 ➡ Upside down 7
Value 15 — Binary 1111 (Not used)
🎉 TADAAAAAA!!! The 8 flavors are explained! Two are binary palindromes that look the same upside down (0110 and 1001), and that leaves six flavors that have an upside-down twin! It all makes sense!
I ran to the toy and quickly inserted a non-palindrome disc upside down to be sure. It worked as expected; mystery solved!
![](https://miro.medium.com/v2/resize:fit:2596/1*BLBNlgP2-_JOdy3z42vQ8Q.jpeg)
![](https://miro.medium.com/v2/resize:fit:2578/1*rJkcH_Uv8yVWg0kmzk5NcA.jpeg)
I’ve never thought of combinations as mirror images of binary! Thanks, random children’s toy!
If you enjoyed this article, you’ll enjoy another post in the same spirit about Xmas countdown dice! Don’t forget to clap and share!
![](https://miro.medium.com/v2/resize:fit:700/0*AeqGEsoeUgZ4X3NG.png)
Gant Laborde is a co-owner and Chief Innovation Officer at Infinite Red, published author, adjunct professor, worldwide public speaker, and mad scientist in training. Clap/follow/tweet or visit him at a conference.