# Try to Permute

Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?

I tried and ended up with no answer.

Note by Rashmi B K
5 years, 3 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:

We can use complementary counting.

There are $$26\cdot 25\cdot 24$$ passwords total.

There are $$15\cdot 14\cdot 13$$ passwords without any letters symmetric.

Therefore, there are $$26\cdot 25\cdot 24-15\cdot 14\cdot 13=12870$$ passwords with at least one symmetric letter.

- 5 years, 3 months ago

Thanks !

- 5 years, 3 months ago

Z is not a symmetric letter ;)

- 5 years, 3 months ago

Maybe Y was intended?

- 5 years, 3 months ago

Ya ! It is Y. Sorry for the mistake !

- 5 years, 3 months ago