How high can you count on one hand???

Factual Questions
1

At a party once a guy bragged that he could count up to x on one hand.

“Nah-uh!” we all protested “you’ve only got five fingers. How could you possible count as high as x?”

He then put on a strange show of flipping up various fingers then retracting them as he counted up to x. The idea was that each finger did not represent a thing to be counted (one finger equals 1, two fingers equals 2, three fingers equals 3, four fingers equals 4, five fingers equals 5, and finished), but rather it was the number of combinations of fingers that could be extended that leads us up to x.

I’ve been trying to remember how he did it, but the problem is I don’t remember was x was.

So far I’ve come up with 23 (24 if you count having zero fingers extended- should you?).
But I think the guy at the party got higher. Try as I may, I can’t get any higher than 23- but it may be that I just confuse myself in the process (sometimes I can’t get to 23), so I come to the SDMB for help.

He explained the combinations as representing binary code. If a finger was not extended it was a zero, if it was extended it was a 1. So this would be easy to figure out if you know anything about binary, or at least how to calculate the possible variations of having two possible figures within five total digits. Unfortunately, I don’t know any of this (in fact the true math experts of the SDMB may be lost in my layman’s gibberish).

Anyway, here are the 23 that I came up with (displayed as each digit representing a finger, thumb on the right and pinky on the left. An extended finger is a 1, a nonextended finger is a 0):

00001
00010
00100
01000
10000
00011
00111
01111
11111
00110
01110
11110
01100
11100
11000
00101
01001
10001
01011
11011
01010
10010
10100
Also, the only order I’ve got here is just what I’ve come up with to try to help myself to not repeat any. I don’t actually know the correct order that these numbers should be in. If you could help with that, it would be appreciated.

How high can you count using both hands???

2

Partly it depends on his technique. In theory, having fingers either extended or folded leads to two choices for each of five fingers, thus 32. Your skill at extending your ring finger while folding your middle may vary.

Then there’s the fact that there’s more than one joint to bend on each finger. Let’s say you can independently bend one knuckle on each finger (that’s all I can do). Then you’ve got two choices for each of ten joints, which lets you count to 1024.

3

You can count to any arbitrary number, if you’re willing to give up counting by ones. Want to count to 4,000,000? OK, my thumb represents 4,000,000.

Heh.

4

You have almost re-invented binary counting, but you got the order a little wrong. FWIW, I have been counting up to 1023 using both hands for a long time. :slight_smile:

Counting in binary is the same as counting in decimal, you just have to remember that you only have two digits instead of ten. With five places, you have (from right to left) a ones place, a twos place, a fours place, an eights place and a sixteens place. Like in decimal, you add one to the rightmost column, bumping the next one to the left when you run out of digits. Thus, the correct order is:

00000
00001
00010
00011
00100
00101
00110
00111
01000
01001
01010
01011
01100
01101
01110
01111
10000
10001
10010
10011
10100
10101
10110
10111
11000
11001
11010
11011
11100
11101
11110
11111

5

Thanks for the help.

Actually, once I started typing it out in “ones” and “zeros” it started to make sense, I just hadn’t made sense of it before finishing my post. When I’ve tried it on my fingers I didn’t see the fingers as ones and zeros, so I just tried to come up with a system that would help me avoid repeating myself.

So it’s 32, counting “00000” as 1? Gotta love math GQs. They fulfill the “factual answer” requirement with no wiggle room.

And, yes, we were only counting fully extended digits vs. fully folded digits and each digit as 1.

6

There are 32 possible combinations, but (probably because I am a programmer) I prefer to count 00000 as zero, and 11111 as 31. If you want to start everything at one, be my guest. :cool:

7

I’ve played around a bit counting in base 3, with a half-extended finger representing 1 and a fully extended finger 2, but that’s tricky. Maybe if I were willing to practice more, I’d be able to do it, but being able to count to 31 on one hand is usually good enough.

8

I’ve played around a bit counting in base 3, with a half-extended finger representing 1 and a fully extended finger 2, but that’s tricky. Maybe if I were willing to practice more, I’d be able to do it, but being able to count to 31 on one hand is usually good enough.

9

Bengalis use their thumbs to count to four on each finger (one for each “crease” plus the tip), for a total of 16.

Using the Chisanbop method, you can use all 10 of your fingers to count to 99.

10

Fun counter-geek party tricks …

“I can count to 1023 on my fingers!”
“No you can’t.”
“Sure I can, wanna see?”
“Yeah, show me, um, how about 132?”
“OK!”
…
“Same to you, jerk!”

:smiley:

11

You’ve also got your wrist, which you can use to represent another bit, so that brings you up to 64 with one hand.

You could also hold your hand up high or down low for another bit, so you’re up to 128.

12

I can count to 21 if I’m naked! :smiley: :smiley: :smiley: :smiley: :smiley:

13

"Come into this room. You see it is very small. But see, in the midst of it there is a girl, perhaps about eighteen years old. What a terrible dress she has on — her dress is made of fire. On her head she wears a bonnet of fire. It is pressed down close all over her head; it burns her head; it burns into the skin; it scorches the bone of the skull and makes it smoke. The red hot fiery heat goes into the brain and melts it… You do not, perhaps, like a headache. Think what a headache that girl must have. But see more. She is wrapped up in flames, for her frock is fire. If she were on earth she would be burnt to a cinder in a moment. But she is in Hell, where fire burns everything, but burns nothing away. There she stands burning and scorched; there she will stand for ever burning and scorched! She counts with her fingers the moments as they pass away slowly, for each moment seems to her like a hundred years. As she counts the moments she remembers that she will have to count them for ever and ever."
“The Sight of Hell,” Rev. John Furniss, C.S.S.R.

14

Ah, yes, nothing like a little religion to lighten the mood … Seems obvious to me why so many folks believe …
Back to the math, If you really want to get complicated, in addition to the simple 10 fingers open/closed = 2^10 =1024, you can generate another 8 bits by holding the fingers together or apart and considering the gaps between fingers as bits. eg for apart = 1, the right-handed Vulcan salute gives additional bits of t1i0m1r0p where “timpr” indicates thumb, index, middle, ring, pinky.

This gives 2^9 = 512 for one hand & 2^18 = 256K = 262,144 decimal for two hands. Add in the bent wrist trick and we get 1024 per hand and 1Meg per pair.

The dexterity required to actually count this way reliably is beyond me, but it does look either waay cool, or like gangsta signs depending on your viewpoint.

Now all we gotta do is figure out a good way to multiply the value on one hand by the value on the other. If you could do calcs reliably that way you’d hardly need a calulator. Doing the basic 4 operations with 3 sigfigs of precision was good enough to get to the Moon.

15

I totally want to party with you guys…

16

Well, I can bend my fingers at both joints between distal and middle phalanges, and between middle and proximal. (Yes, I was the coolest person in the world in elementary.) (except the hallux, of course)

That’s 2x3[sup]4[/sup], right? That’s… umm, I can count to 486.

17

Truth be told, this is the only response I was hoping for when I started this Thread. :smiley: