Largest palindrome product: Difference between revisions

</pre>

=={{header|Quackery}}==

The largest product of two 3 digit numbers is 999*999 = 998001.

The smallest product of two 3 digit numbers is 100*100 = 10000.

Therefore we need only consider 6 and 5 digit palindromic numbers.

Considering 6 digit palindromic numbers:

The largest is 999999.

The smallest is 100001.

These can be costructed from the numbers 100 to 999.

Therefore there are 899 6 digit palindromic numbers.

The same applies to 5 digit palindromic numbers:

The largest is 99999.

The smallest is 10001.

These can be costructed from the numbers 100 to 999.

Therefore there are 899 5 digit palindromic numbers.

'''Method:'''

* Construct the 6 digit palindromic numbers in reverse numerical order.

* Test each one to see if it is divisible by a 3 digit number with a 3 digit result, starting with 999.

* If it is, the solution has been found.

* If no solution found, consider 5 digit palindromes.

A six digit solution was found, and as it was found virtually instantaneously I did not feel that any optimisations were necessary.

I went on to find the largest five digit soultion, even though the task did not call for it, as it was a trivial exercise.

<syntaxhighlight lang="Quackery"> [ [] swap

[ 10 /mod

rot join swap

dup 0 = until ]

drop ] is ->digits ( n --> [ )

[ behead swap

witheach

[ swap 10 * + ] ] is ->number ( [ --> n )

[ ->digits

dup reverse join

->number ] is evenpal ( n --> n )

[ ->digits

dup reverse

behead drop join

->number ] is oddpal ( n --> n )

[ 2dup mod 0 != iff

[ 2drop false ]

done

/ 100 1000 within ] is solution ( n n --> b )

false

899 times

[ i 100 + evenpal

899 times

[ dup i 100 +

solution if

[ dip not

conclude ] ]

over iff

[ nip conclude ]

else drop ]

dup iff

[ say "Six digit solution found: " echo ]

else

[ drop say "No six digit solution found." ]

cr

false

899 times

[ i 100 + oddpal

899 times

[ dup i 100 +

solution if

[ dip not

conclude ] ]

over iff

[ nip conclude ]

else drop ]

dup iff

[ say "Five digit solution found: " echo ]

else

[ drop say "No five digit solution found." ]

</syntaxhighlight>

{{out}}

<pre>Six digit solution found: 906609

Five digit solution found: 99899