How high can you count on your fingers? (Spoiler: much higher than 10) – James Tanton

By | August 24, 2019

How high can you count on your fingers? It seems like a question
with an obvious answer. After all, most of us have ten fingers, or to be more precise, eight fingers and two thumbs. This gives us a total of ten digits
on our two hands, which we use to count to ten. It’s no coincidence that the ten symbols
we use in our modern numbering system are called digits as well. But that’s not the only way to count. In some places, it’s customary to
go up to twelve on just one hand. How? Well, each finger is divided
into three sections, and we have a natural pointer
to indicate each one, the thumb. That gives us an easy to way to count
to twelve on one hand. And if we want to count higher, we can use the digits on our other hand to
keep track of each time we get to twelve, up to five groups of twelve, or 60. Better yet, let’s use the sections
on the second hand to count twelve groups of twelve,
up to 144. That’s a pretty big improvement, but we can go higher by finding more
countable parts on each hand. For example, each finger
has three sections and three creases for a total of six things to count. Now we’re up to 24 on each hand, and using our other hand to mark
groups of 24 gets us all the way to 576. Can we go any higher? It looks like we’ve reached the limit
of how many different finger parts we can count with any precision. So let’s think of something different. One of our greatest
mathematical inventions is the system of positional notation, where the placement of symbols allows
for different magnitudes of value, as in the number 999. Even though the same symbol is used
three times, each position indicates a different
order of magnitude. So we can use positional value on
our fingers to beat our previous record. Let’s forget about finger sections
for a moment and look at the simplest case of having
just two options per finger, up and down. This won’t allow us to represent
powers of ten, but it’s perfect for the counting system
that uses powers of two, otherwise known as binary. In binary, each position has double
the value of the previous one, so we can assign
our fingers values of one, two, four, eight, all the way up to 512. And any positive integer,
up to a certain limit, can be expressed
as a sum of these numbers. For example, the number seven
is 4+2+1. so we can represent it by having
just these three fingers raised. Meanwhile, 250 is 128+64+32+16+8+2. How high an we go now? That would be the number with all ten
fingers raised, or 1,023. Is it possible to go even higher? It depends on how dexterous you feel. If you can bend each finger just halfway,
that gives us three different states – down, half bent, and raised. Now, we can count using
a base-three positional system, up to 59,048. And if you can bend your fingers
into four different states or more, you can get even higher. That limit is up to you,
and your own flexibility and ingenuity. Even with our fingers in just two
possible states, we’re already working pretty efficiently. In fact, our computers are based
on the same principle. Each microchip consists of tiny
electrical switches that can be either on or off, meaning that base-two is the default way
they represent numbers. And just as we can use this system to
count past 1,000 using only our fingers, computers can perform billions
of operations just by counting off 1’s and 0’s.

100 thoughts on “How high can you count on your fingers? (Spoiler: much higher than 10) – James Tanton

  1. supertuber kid Post author


  2. Alex Butler Post author

    You can 8 digits of base 6 using the sections and creases on each finger, 6^8=1,679,616 numbers

  3. josue alimorong Post author

    I can count to One-Quintillion with my fingers

  4. BZG Post author

    Did you know, in American Sign Language you can easily count up to 999 on 1 hand

  5. FIREFIRE CPB:- The New Beginning! Post author

    Why do I have 4 sections on my little finger?

  6. Anna Deeds Post author

    You could just use sign language and count as high as you want

  7. Triggered Potato Post author

    Only Chernobyl kids remember counting to 100

  8. Walker Cpt Post author

    Why didn't i think of using binary system from the last time ? i like computers and binary

  9. Rari Post author

    Muslims have been using this method for centuries 🙂 to pray. But 4 sections are counted on one finger so it reaches a total of 32 when u read it through twice.

  10. Tristan S G S Post author

    I haven’t watched the vid yet, and right now the highest I can count with two hands is to 59

  11. Lori Wolfcat Post author

    Actually, you can count to 20 on one hand. You didn’t even count the fingertips, which seemed like you would. And you can still count your thumb and it’s crease with your other fingers. And how the heck did you go from 12 to 24 on 1 hand??

  12. ZephyrAlphaOne Post author

    Well, I could say my index finger is +infinity and keep it raised. I win 🙂

  13. Renzoh’s Club Post author

    0:09 This video is mocking me.

    Hint: Pause at that exact time

  14. Vaibhav Divakar Post author

    Just count one finger as a billion…. Game over…. You don't need flexibility folks!

  15. Gjana Larson Post author

    Dude I learn this at school and now it's in my recommended

  16. Kylie Raiber Post author

    You can also count on one hand with sign language.

  17. k Post author

    The part where he divides his fingers into three…. HE DIDNT USE HIS THUMB!!! u can count till 15 with that method..

  18. wEirDOpANdAoWl Post author

    Imma stick with the classic 10 fingers thank you very much

  19. RumboRupy Post author

    20? fingers and nails

    edit:50 cause you count nails and fingers on one hand and count how many times you get to ten

    edit edit : or you can count each finger as infinite

  20. Flamin' Up Post author


    Ted-ed: You can count up to infinite with your fingers

  21. Aaron Parker Post author

    0:09 pause the video she is holding up the middle finger

  22. Bazooka Rainbow Juice Post author

    I can count more than 100 and my teacher says I can't count more than 10 on my fingers

  23. The Rtist Post author

    132 ! (If anyone understood that ily 🙂

    Edit : now that I’ve scrolled down the comment section, i can see others beat me to that pun .

  24. Piglet John Post author

    Thumbs are fingers! They have the same amount of joints as our other fingers if you include the really far back knuckle

  25. Faraaz Ibtisham Post author

    In (I think) Islamic counting, we use our "finger fold marks" and our nails+ our thumbs too. (I mixed two of your theories to get 1,156)

  26. Sorry I didnt know what to choose Post author

    Why didnt they just say the amount lol.
    Its with 2 states and 10 fingers 2 to the power of 10 and that minus one because we include 0.
    That is 1023.
    3 states 3 to the power of 10 minus 1 = 59048.
    4 states 4 to the power of 10 minus 1 = 1048575.
    and 5 states 5 to the power of 10 minus 1 = 9765624.
    This continues.
    If we would have 5 fingers and two states then it is just 2 to the power of 5 minus 1 = 31.

  27. Brownskikuca Post author

    Thanks, I like to count to 5.2386895e+26 . That is beacuse i made 5 positions. Oh wait that is illegal… I HAVE FRACTIONS!!!!!!!!!!!!!

  28. Andy Zhou Post author


  29. New3DSLUIGI364 Post author

    I can now count to twelve on my hands. . .

  30. chromosoze's account Post author

    when i pass 10 in my head i just keep track of which tens im in

  31. Mr. Clean Post author

    You could’ve just counted to 100,000,000,000 and all the sections and creases

  32. TXC Rag3 Post author

    WOW. Your least popular video, HAS 2 MILLION VIEWS!!

  33. Chấn Quân Phạm Post author

    The hard part is keeping track ?

  34. A2ZviaBLT Post author

    Fun fact. I've lived at both 0010000100 and 0101010101 in my lifetime

  35. ashish sharma Post author

    Started with practicality and progressed to non-sense just because it can

  36. MiteShake Gaming Post author

    What about using the rare six fingers?

  37. Hunted Edge-Gaming Post author

    We also have something called sign language

  38. Zachary Walker Post author

    I totally thought they would be talking about sign language counting ???

  39. CnCF 0878 Post author

    This made me wonder… At 0:07, what if I made it x0.25.
    I laughed so hard when the hand got middlefingered

  40. Golden Gamer Fox Post author

    alright, so i will answer before the video even starts. you can count up to 1023/1024.

    edit: turns out it was 59048…


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