Est. 1998 — 27 years of woodworking knowledge
Tuesday Puzzle
Running a bit late today.
A number palindrome is one that reads the same frontwards as backwards. For example 4224 reads the same both ways. The sequence:
3, 11, 12, 21, 2, 14, 1, 13
is not of itself a palindrome, however there is a simple formula that can be applied to each number in turn and the resultant numbers form a palindrome. What is the simple formula and what are the numbers that result. (the palindrome)
Solution
I have a solution.
The formula is simple (in fact, couldn't be simpler).
The result is a palindrome, even if an uninteresting one.
But I suspect you are looking for a non-trivial answer.
But just in case you are not, f(x) = 0 for all x, applied to the sequence 3, 11, 12, 21, 2, 14, 1, 13 yields the fascinating palindrome 0,0,0,0,0,0,0,0
I guess that's not what you had in mind? :-)
uuuh, not quite;-)
However, that is good for creative points ;-) (and actually, I guess it is a solution, just not the one I wanted. )_
How about this one
F(x) = the larges prime factor (or 1) in the expansion of the product of the digits in the decimal representation of x
F(3, 11, 12, 21, 2, 14, 1, 13) = 3,1,2,2,2,2,1,3
Again, A solution, but I fear not THE solution.
This is a stumper!
I think
You are making it more complicated than it needs to be. The function needed is not exotic or unknown at all. Most third graders could do the math. ;-)
Uncle!
Re: Uncle!
On this one, I must apologize. There was an error in the source I got this from that I didn't see until I tried it out myself. The third number should be 8, not 12. Then you can multiply by 3 and get the palindrome.
No excuse except that I ran late and just took one from a source I found some time ago and copied it.
Aha
My mistake was that I was trying to (and did with my two wrong answers) preserve the commas as part of the palindrome answer.