Matt Parker's Maths Puzzles #3

README.md

What is this?

This is Pufe's solution to Matt Parker's Maths Puzzles #3 as mentioned on video https://youtu.be/JaXo_i3ktwM

How does it work?

It's a simple ruby program to test every letter combination and find out how many scrabble hands have exactly 46 points total

Why did you do it?

I'm neither good enough at Maths to find a clever way of counting, nor patient enough to do it by hand.

How to run?

You need a ruby interpreter (MacOS usually comes with one) and then run on the command line:

ruby mpmp3.rb < mpmp3.in

I've made the program accept an file describing the tiles, in the format on the website https://think-maths.co.uk just in case someone wants to try with a different language Scrabble Set.

Can I copy your code?

Sure, the code is given as is, you may do whatever with it. I provide no guarantee about its safety. If you wanna get legal about it, license is WTFPL .

mpmp3.in

0 points - _ (x2)
1 point - A (x9), E (x12), I (x9), O (x8), U (x4), L (x4), N (x6), S (x4), T (x6), R (x6)
2 points - D (x4), G (x3)
3 points - B (x2), C (x2), M (x2), P (x2)
4 points - F (x2), H (x2), V (x2), W (x2), Y (x2)
5 points - K (x1)
8 points - J (x1), X (x1)
10 points - Q (x1), Z (x1)

mpmp3.out

138
AFJKQXZ
AHJKQXZ
AJKQVXZ
AJKQWXZ
AJKQXYZ
BBFJQXZ
BBHJQXZ
BBJQVXZ
BBJQWXZ
BBJQXYZ
BCFJQXZ
BCHJQXZ
BCJQVXZ
BCJQWXZ
BCJQXYZ
BDJKQXZ
BFJMQXZ
BFJPQXZ
BGJKQXZ
BHJMQXZ
BHJPQXZ
BJMQVXZ
BJMQWXZ
BJMQXYZ
BJPQVXZ
BJPQWXZ
BJPQXYZ
CCFJQXZ
CCHJQXZ
CCJQVXZ
CCJQWXZ
CCJQXYZ
CDJKQXZ
CFJMQXZ
CFJPQXZ
CGJKQXZ
CHJMQXZ
CHJPQXZ
CJMQVXZ
CJMQWXZ
CJMQXYZ
CJPQVXZ
CJPQWXZ
CJPQXYZ
DFFJQXZ
DFHJQXZ
DFJQVXZ
DFJQWXZ
DFJQXYZ
DHHJQXZ
DHJQVXZ
DHJQWXZ
DHJQXYZ
DJKMQXZ
DJKPQXZ
DJQVVXZ
DJQVWXZ
DJQVXYZ
DJQWWXZ
DJQWXYZ
DJQXYYZ
EFJKQXZ
EHJKQXZ
EJKQVXZ
EJKQWXZ
EJKQXYZ
FFGJQXZ
FGHJQXZ
FGJQVXZ
FGJQWXZ
FGJQXYZ
FIJKQXZ
FJKLQXZ
FJKNQXZ
FJKOQXZ
FJKQRXZ
FJKQSXZ
FJKQTXZ
FJKQUXZ
FJMMQXZ
FJMPQXZ
FJPPQXZ
GHHJQXZ
GHJQVXZ
GHJQWXZ
GHJQXYZ
GJKMQXZ
GJKPQXZ
GJQVVXZ
GJQVWXZ
GJQVXYZ
GJQWWXZ
GJQWXYZ
GJQXYYZ
HIJKQXZ
HJKLQXZ
HJKNQXZ
HJKOQXZ
HJKQRXZ
HJKQSXZ
HJKQTXZ
HJKQUXZ
HJMMQXZ
HJMPQXZ
HJPPQXZ
IJKQVXZ
IJKQWXZ
IJKQXYZ
JKLQVXZ
JKLQWXZ
JKLQXYZ
JKNQVXZ
JKNQWXZ
JKNQXYZ
JKOQVXZ
JKOQWXZ
JKOQXYZ
JKQRVXZ
JKQRWXZ
JKQRXYZ
JKQSVXZ
JKQSWXZ
JKQSXYZ
JKQTVXZ
JKQTWXZ
JKQTXYZ
JKQUVXZ
JKQUWXZ
JKQUXYZ
JMMQVXZ
JMMQWXZ
JMMQXYZ
JMPQVXZ
JMPQWXZ
JMPQXYZ
JPPQVXZ
JPPQWXZ
JPPQXYZ

mpmp3.rb

def read_input(lines)
  letters = []
  lines.each do |line|
    points = line.split[0].to_i
    line.scan(/(.) \(x(\d+)\)/).each do |letter, count|
      letters << {letter: letter, count: count.to_i, value: points}
    end
  end
  letters.sort_by{|x| x[:letter]}
end

def generate(pool, starting_from, target, prefix, count, solutions)
  if count == 7
    if target == 0
      return solutions + [prefix]
    else
      return solutions
    end
  end
  if target >= 0
    starting_from.upto(pool.size-1) do |i|
      if pool[i][:count] > 0
        pool[i][:count] -= 1
        solutions = generate(pool, i, target - pool[i][:value], prefix + pool[i][:letter], count+1, solutions)
        pool[i][:count] += 1
      end
    end
  end
  return solutions
end

def main
  pool = read_input($<.readlines)
  solutions = generate(pool, 0, 46, "", 0, [])
  puts solutions.size
  puts solutions
end

main