πŸ”πŸ”πŸ”πŸ”πŸ”πŸ”πŸ” [challenge] reversal friends πŸ”πŸ”πŸ”πŸ”πŸ”πŸ”πŸ” | Sololearn: Learn to code for FREE!

+17

πŸ”πŸ”πŸ”πŸ”πŸ”πŸ”πŸ” [challenge] reversal friends πŸ”πŸ”πŸ”πŸ”πŸ”πŸ”πŸ”

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

11/14/2017 9:00:02 PM

Oma Falk

32 Answers

New Answer

+17

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

+15

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

+14

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

+13

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

+9

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

+9

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.

+8

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

+8

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

+7

Okay batman

+6

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

+6

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

+5

@mike it is even more crazy! there are only 7 with permutation. 26 * 93 = 62*39 so..... 23*96 = 32 * 69

+5

I found the magic in it ... We can build the numbers just run program - it will explain the mathemagic https://code.sololearn.com/cL03mOs02v3u

+4

@::: BATMAN herezz mine One Liner https://code.sololearn.com/c1q0tvHOiZhO/?ref=app

+4

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

+4

@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.

+4

@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

+3

it works fr 3 digit also... 10 * 3 = 15 * 2 102*315=210*153

+3

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

+3

@sayan are you mathematican?