043.cpp File Reference

The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property. More...

#include <iostream>
#include "043_permutation.h"
#include <set>

Go to the source code of this file.

Functions
unsigned	slice_perm (perm043 &perm, idx begin, idx end)
unsigned long long	sum (set< unsigned > &numbers)
int	main ()

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Detailed Description

The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property.

Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this way, we note the following:

• d2d3d4=406 is divisible by 2
• d3d4d5=063 is divisible by 3
• d4d5d6=635 is divisible by 5
• d5d6d7=357 is divisible by 7
• d6d7d8=572 is divisible by 11
• d7d8d9=728 is divisible by 13
• d8d9d10=289 is divisible by 17

Find the sum of all 0 to 9 pandigital numbers with this property.

Definition in file 043.cpp.

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Function Documentation

unsigned slice_perm	(	perm043 &	perm,
		idx	begin,
		idx	end
	)

extract subset of digits, and convert to integer.

Parameters:

perm	object containing the permutation
begin	starting position
end	ending position

Returns:

an integer having (end-begin) digits.

Definition at line 24 of file 043.cpp.