hallway_riddle.org

Org-mode solution to this riddle.

More to learn about org-mode than to solve the riddle…

1. The product of the 3 numbers is 36.
2. The sum is the hallway number, which Zara knows.
3. The largest number is unique.
4. Zara needed the third clue.

Work out all the factors that produce 36:

product = 36
factors = []

(1..product).each {|x|
  (x..product).each {|y|
    (y..product).each {|z|
      factors << [x, y, z] if x * y * z == product
    }
  }
}

factors

1	1	36
1	2	18
1	3	12
1	4	9
1	6	6
2	2	9
2	3	6
3	3	4

There are only 8 possible results, and these are the sums:

sums = factors.map { |f|
  f + ["="] << f.reduce(:+)
}

1	1	36	=	38
1	2	18	=	21
1	3	12	=	16
1	4	9	=	14
1	6	6	=	13
2	2	9	=	13
2	3	6	=	11
3	3	4	=	10

Since she needed the last clue, and only 1*6*6 and 2*2*9 produce the same result, she must have gone through hallway 13 with the code 229.