# In this question, would dig be 2 inputs, such as 91 and 99? And lim can be any number the user calls?

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champions2015 on 6 Sep 2017
Edited: Jan on 25 Feb 2018
A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99. Write a function that is called this way:
>> n = palin_product(dig,lim);
The function returns the largest palindrome smaller than lim that is the product of two dig digit numbers. If no such number exists, the function returns 0. (Inspired by Project Euler.)
Image Analyst on 6 Sep 2017

Stephen23 on 7 Sep 2017
Edited: Stephen23 on 7 Sep 2017
I know that this is homework, but someone needed to demonstrate how this can be done quite simply, without using slow and unnecessary third-party functions: I believe that champions2015 and future readers deserve to be shown that MATLAB code can be neat, efficient, and straightforward. Note that this code actually does exactly what the question asks for!
function n = palin_product(dig,lim)
n = 0;
V = 10.^dig-1:-1:10.^(dig-1);
for k1 = V
for k2 = V
p = k1*k2;
if p>n && p<lim
s = sprintf('%d',p);
if all(s==s(end:-1:1))
n = p;
end
end
end
end
end
And tested:
>> palin_product(2,10000)
ans = 9009
>> palin_product(2,9009)
ans = 8448
>> palin_product(2,8448)
ans = 8118
>> palin_product(2,8118)
ans = 8008
>> palin_product(2,8008)
ans = 7227
Stephen23 on 14 Sep 2017
Thank you Jan Simon, that is a very neat idea.

the cyclist on 6 Sep 2017
I would interpret it as follows.
You are trying to find p1 * p2 = n.
• lim is any number the user chooses (just as you guessed). The output, n, must be smaller than lim.
• dig is the number of digits that p1 and p2 each have. For example, if p1=91, and p2=99, then dig=2, because they are 2-digit numbers.

Image Analyst on 6 Sep 2017
Hint:
n = 9009
s = sprintf('%d', n)
flipped_s = fliplr(s)

John BG on 7 Sep 2017
Edited: Jan on 25 Feb 2018
hi champions2015
the following is a slight variation of what's been asked, this function
• returns the nearest palindrome to the input
• also calculates the 2 numbers of digit length dig that multiplied are lim
• if the input is already a palindrome, it decomposes as requested lim, not seeking any smaller palindrome.
clear all;clc
lim2=8448
dig=2
function [lim r1 r2]=palin_product(dig,lim2)
r1=0;r2=0;
ispal=0;
decom=1;
lim=lim2 % keep start value in lim2, modify lim
while decom
ispal=0;
while ~ispal % find next symmetric integer below input lim2
L1=num2str(lim);
n1=1;n2=length(L1);
while L1(n1)==L1(n2) && n1<=floor(length(L1)/2)
n1=n1+1;n2=n2-1;
end
if L1(n1)==L1(n2) ispal=1; end
if ~ispal lim=lim-1; end
end
s1=10^(dig-1);s2=str2num(repmat('9',1,dig)); % find whether found lim can be decomposed
S=[s1:1:s2];
L=combinator(numel(S),dig,'p','r');
p=1;
s1=S(L(p,1));s2=S(L(p,2));
while ~(s1*s2==lim) && p<length(L)
s1=S(L(p,1));s2=S(L(p,2));
p=p+1;
end
if p<=length(L) && s1*s2==lim
r1=s1;r2=s2
end
if r1==0 && r2==0
lim=lim-1;
end
if r1*r2>0
decom=0;
end
end
end % function
.
the most recent version of the function combinator and its support functions are all packed and freely available from
combinator_update.zip and palin_product.m are both attached to this answer.
.
John BG
##### 2 CommentsShowHide 1 older comment
John BG on 7 Sep 2017
Edited: John BG on 7 Sep 2017
Hi Champions2015
When the input is already is such palindrome that can be decomposed as requested, why would you want to seek a smaller palindrome that can be decomposed into 2 figures of digit length dig?
My function also calculates the requested digit dig length decomposition.