Magic numbers
Magic numbers are polydivisible numbers in base 10. A polydivisible number is a number where the first n digits are evenly divisible by n.
Magic numbers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
E.G. The number 1868587 is a magic number (is polydivisible in base 10.)
1 ÷ 1 = 1
18 ÷ 2 = 9
186 ÷ 3 = 62
1868 ÷ 4 = 467
18685 ÷ 5 = 3737
186858 ÷ 6 = 31143
1868587 ÷ 7 = 266941
There is a finite number of magic numbers.
- Task
- Write a routine (subroutine, function, procedure, generator, whatever it may be called in your language) to find magic numbers.
- Use that routine to find and display how many magic numbers exist.
- Use that routine to find and display the largest possible magic number.
- Count and display how many magic numbers have 1 digit, 2 digits, 3 digits, ... for all magic numbers.
- Find and display all of the magic numbers that are minimally pandigital in 1 through 9. (Contains each digit but only once.)
- Find and display all of the magic numbers that are minimally pandigital in 0 through 9.
Zero (0) may or may not be included as a magic number. For this task, include zero.
- See also
Raku
my \Δ = $ = 1;
my @magic = flat 0, [1..9], {last if .not; ++Δ; [(.flat X~ 0..9).grep: * %% Δ]}…*;
put "There are {@magic.eager.elems} magic numbers in total.";
put "\nThe largest is {@magic.tail}.";
put "\nThere are:";
put "{(+.value).fmt: "%4d"} with {.key.fmt: "%2d"} digit{1 == +.key ?? '' !! 's'}"
for sort @magic.classify: {.chars};
{
my $pan-digital = ($_..9).join.comb.Bag;
put "\nAll magic numbers that are pan-digital in $_ through 9 with no repeats: " ~
@magic.grep( { .comb.Bag eqv $pan-digital } );
} for 1, 0;
- Output:
There are 20457 magic numbers in total. The largest is 3608528850368400786036725. There are: 10 with 1 digit 45 with 2 digits 150 with 3 digits 375 with 4 digits 750 with 5 digits 1200 with 6 digits 1713 with 7 digits 2227 with 8 digits 2492 with 9 digits 2492 with 10 digits 2225 with 11 digits 2041 with 12 digits 1575 with 13 digits 1132 with 14 digits 770 with 15 digits 571 with 16 digits 335 with 17 digits 180 with 18 digits 90 with 19 digits 44 with 20 digits 18 with 21 digits 12 with 22 digits 6 with 23 digits 3 with 24 digits 1 with 25 digits All magic numbers that are pan-digital in 1 through 9 with no repeats: 381654729 All magic numbers that are pan-digital in 0 through 9 with no repeats: 3816547290