perplexus.info :: Numbers : Numbers and their inversions

Numbers and their inversions (Posted on 2024-05-23)

We will be dealing with two-digit numbers non divisible by 11.
For each such number A there will exist another A’, a number created by inverting the digits of A so 45’=54, 87’=78.
Take for example 2 numbers 36 & 84: their product is the same as the product of those numbers inverted i.e. 63*48.

Find all the couples possessing such feature i.e. AB=(A')*(B').
Rem: to preserve conformity present the smallest number on the LHS of the equation - like 12*42=21*24.

See The Solution Submitted by Ady TZIDON

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Puzzle Thoughts

| Comment 4 of 5 |

There are precisely 28 non trivial solutions. They are:

12*42 = 21*24

12*63 = 21*36

12*84 = 21*48

13*62 = 31*26

13*93 = 31*39

14*82 = 41*28

21*24 = 12*42

21*36 = 12*63

21*48 = 12*84

23*64 = 32*46

23*96 = 32*69

24*63 = 42*36

24*84 = 42*48

26*31 = 62*13

26*93 = 62*39

28*41 = 82*14

31*39 = 13*93

32*46 = 23*64

32*69 = 23*96

34*86 = 43*68

36*42 = 63*24

36*84 = 63*48

39*62 = 93*26

42*48 = 24*84

43*68 = 34*86

46*96 = 64*69

48*63 = 84*36

64*69 = 46*96

Edited on May 27, 2024, 10:57 pm

Posted by K Sengupta on 2024-05-24 02:41:10

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info