# Prove this if you can!

If you ask someone to choose ten random digits (not including 0) and multiply them all together, then to tell you all but one of the digits of the answer, you can predict the remaining digit.

Good luck proving it!

Note by Victor Loh
4 years, 5 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

What do you mean? If I choose ten '1's, their product is 1. So I will tell that person nothing (all but one). However there are many possible digits.

- 4 years, 5 months ago

If there were a dislike button I would have pressed it.

- 4 years, 3 months ago

Let the random digits be $$a_1, a_2, a_3, \ldots, a_{10}$$ $$\Huge\mbox{NOT}$$ respectively, where $$a_{10}$$ is the digit not told to you.

The product will be $$P=a_1a_2a_3\ldots a_{10}$$, and the digits told to you will be $$a_1, a_2, a_3, \ldots, a_9$$.

The remaining digit is obtained by dividing $$P$$ by $$a_1, a_2, a_3, \ldots, a_9$$ one by one, which equals to $$a_{10}$$.

- 4 years, 5 months ago

This is an extremely fun question, as well as easy. :)

- 4 years, 5 months ago