What is a thorough method to manually generate a random number between $1$ and $100$?

Question

The other day, I got an idea. I would like to generate a random number between $1$ and $100$ , however by hand. You often want to use these random numbers to play games or even for practical purposes.

And only using simple tools like a desk clock and pen and paper.

What might be a reliable way to do this?

Toss the clock in the air and see which side it comes down on :-). Repeat 7 times, and form a binary number. Ignore if the number is 100 or larger. — copper.hat, Jan 05 '15 at 17:31
What sort of distribution would you like? By most definitions, you could have a random variable with only one possible value (i.e., a one-element state space), even if it is somewhat uninteresting. So, write "$42$". Then, the number you wrote is your random number. — KSmarts, Jan 05 '15 at 17:45
The method suggested by @copper.hat reminds me of the apocryphal story of how to determine the height of a building using a barometer. :-) — Jens, Mar 13 '17 at 22:40
@Jens- haha that's hilarious. Sometimes the answer is closer than we think eh — Caffeinated, Mar 17 '17 at 15:56

score 9 · Answer 1 · answered Jan 05 '15 at 17:31

9

Take your paper and cut it into $100$ smaller (equal sized) pieces. Write each of the numbers $1$ through $100$ on the pieces. Then mix up the pieces and pick one at random.

If you don't want to do $100$ slips, use $10$ slips, labelled $0,1,...,9$. Pick twice with replacement for the two digits. If you get $00$, that's $100$.

answered Jan 05 '15 at 17:31

paw88789

40,402

2

I think he should cut & fold the paper into a pentagonal trapezohedron (aka, a d10), and use it as percentile dice. – KSmarts Jan 05 '15 at 17:48
That would be very cool! – paw88789 Jan 05 '15 at 18:45
@KSmarts - How would you do this? – Caffeinated Mar 10 '17 at 14:37

score 5 · Accepted Answer · 2017-03-18T20:55:28.633

5

A method I've always liked is to put down a bunch of parallel lines on paper and pick one somewhere in the middle, and count how many lines are on the left of it, and take that $\mod n$. The number of lines you start with of course depends on $n$ (it should be a lot more than $n$) but this is okay, since we don't need very high numbers $n$ anyway. In the case of $100$, we take $n=2$, $n=2$, $n=5$ and $n=5$, and construct the random number from these results.

edited Mar 18 '17 at 20:55

answered Mar 13 '17 at 13:00

i need a bit of coffee to understand this one - will revisit in mornin – Caffeinated Mar 17 '17 at 04:12
I liked this one because it seemed a more elegant solution, fast to do. – Caffeinated Mar 17 '17 at 14:34

score 2 · Answer 3 · answered Mar 14 '17 at 00:36

You can find printable paper dice templates on the 'net:
http://www.timvandevall.com/templates/printable-paper-dice-template

If you don't a model with as many sides as you need,
you can always create your own in Blender,
then export a paper model by way of this pepakura script:
https://wiki.blender.org/index.php/Extensions:2.6/Py/Scripts/Import-Export/Paper_Model

score 0 · Answer 4 · answered Mar 14 '17 at 20:54

Step 1 : Put your hand on top of a piece of paper.

Step 2 : With the second hand, grab your pen and stab the first hand with it.

Step 3 : You bleed, look at your clock so you can tell the time of the accident when you call for help.

Step 4 : Mesure the area of paper covered in blood.

Step 5 : Compute ${\text{area of paper covered in blood}\over\text{total area of paper}}\cdot100$

Congratulation, that's how you generate a random number by hand.

What is a thorough method to manually generate a random number between $1$ and $100$?

4 Answers4

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