Brain Teasers
Numbers and Their Reversion
If you add 9 and 9 you get 18, and if you multiply 9 by 9 you get 81 (the reverse of 18). There are 2 more pairs of numbers with the same characteristics and where the result is two-digit:
24 + 3 = 27 and 24 * 3 = 72
and
47 + 2 = 49 and 47 * 2 = 94
But there is only one pair of numbers with a triple-digit result and its reversion.
What are the 2 numbers?
24 + 3 = 27 and 24 * 3 = 72
and
47 + 2 = 49 and 47 * 2 = 94
But there is only one pair of numbers with a triple-digit result and its reversion.
What are the 2 numbers?
Hint
One number has 1 digit and the other has 3.Answer
The numbers are 497 and 2:497 + 2 = 499
and
497 * 2 = 994
Hide Hint Show Hint Hide Answer Show Answer
What Next?
View a Similar Brain Teaser...
If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.
Solve a Puzzle
Comments
very cool.
Superb teaser. Took me a lot of hard work to get it. Cool.
Thanks a lot! I am very pleased to hear that you like it. -Gerd
For anyone who cares...
There is a pattern in this. If the second number is 2, and the first number is 4, how ever many 9's, and a 7. So if your ever looking for the 10 digit number, it is 4999999997 and the other number is 2. ;)
There is a pattern in this. If the second number is 2, and the first number is 4, how ever many 9's, and a 7. So if your ever looking for the 10 digit number, it is 4999999997 and the other number is 2. ;)
And then there's a special case when you choose to express 2-digit numbers as 3-digit numbers with a leading zero: 5+26=031 and 5*26=130. (Possibly others too.)
That wasn't really a teaser. To mathamatical to me. But is was good one!
Cool. I didn't take it far enough to find the pattern that theone found, but I did find it pretty quickly by starting with numbers similar to the two-digit numbers. Was clear it would be a single-digit and a similar three-digit.
I managed to solve it with scip (a linear, mixed integer and nonlinear programming solver). Here is the tiny model file that I used, for anyone who might be interested to play with it.
##########
##########
var n1 integer >=1 =1 =0 =0 =0 = 1; # the result has to be a 3-digit number
subto rev: e >= 1; # ditto for the reversion
##########
##########
var n1 integer >=1 =1 =0 =0 =0 = 1; # the result has to be a 3-digit number
subto rev: e >= 1; # ditto for the reversion
It looks like the scip model code that I posted in my previous comment didn't make it through the comment processing routine and was badly mutilated. For anyone interested it is available at https://pastebin.com/x8VXzDnn
To post a comment, please create an account and sign in.
Follow Braingle!