🔁🔁🔁🔁🔁🔁🔁 [challenge] reversal friends 🔁🔁🔁🔁🔁🔁🔁

Question

Two two-digit numbers are reversal friends, if the product does not change even if each number reverses its digits.
Example : 36 * 84 = 3024
reverse the digits: 63 * 48 = 3024

Challenge: find all reversal friends except trivial solutions like

11 * 22 -> aa * bb
13 * 31 -> ab* ba

have fun, all languages are welcome

Answer 1

@Batman Nice observation! How on Earth would you come up with that magic? 😂

Answer 2

Here's my C# implementation! ✌

There are 28 pairs which satisfy the requirements! I hope to make a generic solution for any number of digits with cleaner presentation but this is what I got now. Enjoy~ ❤

https://code.sololearn.com/cZ78EFF9j8Q3/?ref=app

Answer 3

Here's my try in Ruby 😊
https://code.sololearn.com/cWLNNU5IDG6u/?ref=app

Answer 4

Thank you for your the challenge.
Here's my try :
https://code.sololearn.com/c7u3BWTfKE1J/?ref=app

Answer 5

Really all? There may be a lot of them, there should be a limit

Answer 6

friends... very cool solutions!
thanks very much!
I aak myself, if there is a way not to check ALL possibilities.
and indeed there is a pattern.

3*8 =24
6*4 =24

68 * 43 = 86 * 34

2*9 =18
6*3 =18
26*93 = 62*39

i am not yet done with it.

Answer 7

My try
https://code.sololearn.com/c326gU1eGdrV/?ref=app

Answer 8

https://code.sololearn.com/cfJJoie05A1q/?ref=app

Answer 9

Okay batman

Answer 10

@yerucham yes really all.
The constraint is, that the numbers only have two digits. So there are still a lot but less than 1000.

Answer 11

another py

https://code.sololearn.com/ck4rda1L9X5U/?ref=app

Answer 12

@mike it is even more crazy!
there are only 7 with permutation.

26 * 93 = 62*39

so.....

23*96 = 32 * 69

Answer 13

I found the magic in it ... We can build the numbers
just run program - it will explain the mathemagic

https://code.sololearn.com/cL03mOs02v3u

Answer 14

@::: BATMAN
herezz mine
One Liner

https://code.sololearn.com/c1q0tvHOiZhO/?ref=app

Answer 15

My Java solution to this problem. I have removed all of the simple solutions like 11 * 22 == 22 * 11 and also made sure not to print repeated values like 12 * 42 (with 21 * 24) and then later 42 * 12 (with 24 * 21) <-- spoiler alert :)

Total unique pairs: 14!!

https://code.sololearn.com/c9ZcYBvfU5Qg/#java

Answer 16

@Zephyr thank you!
actually i cant remember what I drunk before.
But suddenly I had a genius moment.
I very much like patterns and I like programming for testing and finding patterns.

Answer 17

@sayan here is the proof:
I a*b = c*d =>

II (10a + c)* (10b + d) =
(10c+a) * (10d + b)

=100ab + 10bc + 10ad + cd =
100cd + 10ad + 10bc + ab

with I

= 100 ab + 10ad + 10bc +cd

the form is terrible but:

qed

Answer 18

it works fr 3 digit also...

10 * 3 = 15 * 2

102*315=210*153

Answer 19

@sayan yippie!!!
can you make a prog?

Answer 20

@sayan are you mathematican?