user
Iterated digits squaring introduces RC the Project Euler Task #92. Combinations with repetitions introduce RC to the concept of generating all the combinations with repetitions of n types of things taken k at a time.

The purpose of this task is to combine these tasks as follows:

:   The collections of k items will be taken from [0,1,4,9,16,25,36,49,64,81] and must be obtained using code from Combinations with repetitions. The collection of k zeroes is excluded.
:   For each collection of k items determine if it translates to 1 using the rules from Iterated digits squaring
:   For each collection which translates to 1 determine the number of different ways, c say, in which the k items can be uniquely ordered.
:   Keep a running total of all the values of c obtained
:   Answer the Project Euler Task #92 question (k=7).
:   Answer the equivalent question for k=8,11,14.
:   Optionally answer the question for k=17. These numbers will be larger than the basic integer type for many languages, if it is not easy to use larger numbers it is not necessary for this task.
assistant
(formerly Perl 6)

**Translation of**: Kotlin

```
use v6;

sub endsWithOne($n --> Bool) {
   my $digit;
   my $sum = 0;
   my $nn = $n;
   loop {
      while ($nn > 0) {
         $digit = $nn % 10;
         $sum += $digit²;
         $nn = $nn div 10;
      }
      ($sum == 1) and return True;
      ($sum == 89) and return False;
      $nn = $sum;
      $sum = 0;
   }
}

my @ks = (7, 8, 11, 14, 17);

for @ks -> $k {
   my @sums is default(0) = 1,0;
   my $s;
   for (1 .. $k) -> $n {
      for ($n*81 ... 1) -> $i {
         for (1 .. 9) -> $j {
            $s = $j²;
            if ($s > $i) { last };
            @sums[$i] += @sums[$i-$s];
         }
      }
   }
   my $count1 = 0;
   for (1 .. $k*81) -> $i { if (endsWithOne($i)) {$count1 += @sums[$i]} }
   my $limit = 10**$k - 1;
   say "For k = $k in the range 1 to $limit";
   say "$count1 numbers produce 1 and ",$limit-$count1," numbers produce 89";
}

```

Output:

```
For k = 7 in the range 1 to 9999999
1418853 numbers produce 1 and 8581146 numbers produce 89
For k = 8 in the range 1 to 99999999
14255666 numbers produce 1 and 85744333 numbers produce 89
For k = 11 in the range 1 to 99999999999
15091199356 numbers produce 1 and 84908800643 numbers produce 89
For k = 14 in the range 1 to 99999999999999
13770853279684 numbers produce 1 and 86229146720315 numbers produce 89
For k = 17 in the range 1 to 99999999999999999
12024696404768024 numbers produce 1 and 87975303595231975 numbers produce 89
```