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-# Perl Weekly Challenge #135
+# Perl Weekly Challenge #136
 
 You can find more information about this weeks, and previous weeks challenges at:
 
@@ -10,88 +10,64 @@ submit solutions in whichever language you feel comfortable with.
 
 You can find the solutions here on github at:
 
-https://github.com/drbaggy/perlweeklychallenge-club/tree/master/challenge-135/james-smith/perl
+https://github.com/drbaggy/perlweeklychallenge-club/tree/master/challenge-136/james-smith/perl
 
-# Task 1 -  Middle three digits
+# Task 1 -  Two friendly
 
-***You are given an integer. Write a script find out the middle 3-digits of the given integer, if possible otherwise throw sensible error.***
+***You are given 2 positive numbers, `$m` and `$n`. Write a script to find out if the given two numbers are "Two friendly".***
 
-## The solution
+*Two positive numbers, `m` and `n` are two friendly when `gcd(m, n) = 2 ^ p` where `p > 0`. The greatest common divisor (gcd) of a set of numbers is the largest positive number that divides all the numbers in the set without remainder.*
 
-Obviously using `substr $n, ??, 3` will give a 3-digit chunk of a number - so what are the errors...
+## The solution
 
- * Not an integer - doesn't match `/^-?\d+$/`
- * Less than 3 digits - length less than 3
- * Does not have a unique "central 3-digits" *i.e.* has even length
+The logic of our solution is (1) find the GCD; (2) check they are not co-prime (GCD = 1); (3) The GCD is a power of 2
 
-The value of the `??` is the expression above - `( length number - 3 ) / 2`
+We can test the last case by converting the GCD into binary - and checking to see if it has the form `10+`. Alternatively we can use `&` and `>>=` to remove trailing zeros.
 
 All that gives us the simple function....
 
 ```perl
-sub middle3 {
-  my $n = shift;
-  return 'Not a number' unless $n =~ m{^-?\d+$};
-  my $l = length( $n = abs $n );
-  return $l < 3 ? 'Too short'
-       : $l % 2 ? substr $n, ( $l - 3 ) / 2, 3
-       :          'Even digits'
-       ;
+sub friendly {
+  my($a,$b) = @_;
+  ($a,$b) = ($b,$a%$b) while $b; ## Compute GCD
+  return 0 if $a == 1;           ## Co-prime not friendly
+  $a>>=1 until $a&1;             ## Remove trailing 0s
+  return $a == 1 ? 1 : 0;        ## Friendly iff
 }
-```
-
-It is possible to compact this slightly - buy 1 - assuming `$n` is an integer, and then rewriting `($l-3)/2` as `$l/2-1` - which is good enough for the `substr` to work.
 
-```perl
-sub middle3compact {
-  my$l=length(my$n=abs$_[0]);
-  $l<3?'Too short':$l%2?substr$n,$l/2-1,3:'Even digits'
-}
 ```
 
-# Task 2 - Validate SEDOL
+# Task 2 - Fibonacci Sequence
 
-***You are given 7-characters alphanumeric SEDOL. Write a script to validate the given SEDOL. Print 1 if it is a valid SEDOL otherwise 0.***
+***You are given a positive number `$n`. Write a script to find how many different sequences you can create using Fibonacci numbers where the sum of unique numbers in each sequence are the same as the given number. ***
 
 ## Solution
 
-You find about SEDOL (Stock Exchange Daily Official List) numbers on Wikipedia at https://en.wikipedia.org/wiki/SEDOL.
-
-The consist of 6 digits/consonants + a checksum digit. The weighted sum of the 6 digits + the checksum is a multiple of 10.
-The weights are 1, 3, 1, 7, 3 and 9 for the six digits and 1 for the checksum.
-
-We have to:
- * validate the number is of valid format for a SEDOL number - 6 numbers or consonants & a single number.
- * compute the weighted sum (using ord to convert the B-Z characters to their numeric equivalends)
- * check to see if it is a multiple of 10
-
+There are two bits to this:
+ * get a list of fibonacci numbers `<= $n`. Easier to find list up to the first fibonnaci number `> $n`.
+   * We have a cache of the fibonnaci numbers - we just need to extend it to include all those fibonnaci numbers below `$n` (if required).
+ * get a list of sums of these numbers which equal `$n`
+   * We call a generic "get-sum" method where we pass in our target number and array of fibonacci numbers
+   * this get-sum method is then call recursively to count the number of totals
+ 
 ```perl
-sub is_sedol {
-## Check correct format... numbers and consonants only
-  return 0 unless $_[0] =~ m{^[0-9B-HJ-NP-TW-Z]{6}\d$};
-
-## Accumulator and weights for each character
-  my( $t, @w ) = qw(0 1 3 1 7 3 9 1);
 
-## Calculate SEDOL sum... note YODA sum -55 + ord $_ to avoid precedence issue
-  $t += ( /\d/ ? $_ : -55 + ord $_ ) * shift @w for split //, $_[0];
+my @fib;
 
-## Return true (1) if total modulo 10 is 0, and false (0) otherwise
-  return $t % 10 ? 0 : 1;
+sub fib_sum {
+  my $n = shift;
+  push @fib, $fib[-1] + $fib[-2] while $n > $fib[-1];
+  return sum( $n, grep { $_ <= $n }  @fib );
 }
-```
 
-Again we can compact the code - by removing spaces and a couple of rewrites:
-
- * replace `unless $x=~//` with `if $x!~//`;
- * flip `@w` and use `pop`.
- * Note `0if` expands as `0 if`.
- 
-```perl
-sub is_sedol_compact {
-  return 0if$_[0]!~/^[\dB-HJ-NP-TW-Z]{6}\d$/;
-  my($t,@w)=qw(0 1 9 3 7 1 3 1);
-  $t+=(/\d/?$_:-55+ord$_)*pop@w for split//,$_[0];
-  $t%10?0:1
+sub sum {
+  local $_;
+  my ( $t, @n ) = @_;
+  return 1 unless $t;
+  return 0 if $t < 0;
+  my $c = 0;
+  $c += sum( $t - $_, @n ) while $_ = shift @n;
+  return $c;
 }
+
 ```