A friend of mine (Hillel Kahana) shared with me a riddle that his 10year old son brought from a math workshop. At first, the riddle sounded easy…
The riddle
You’ve got the first 6 digits 1,2,3,4,5 and 6.
You have to partition the digits into 3 numbers x
, y
and z
where:
x
is a 3digit numbery
is a 2digit numberz
is a single digit number
Such that the multiplication x*y*z
is maximal.
Each digit must be used only once.
For instance, 123*45*6
:
123*45*6
But, obviously we can do better.
Sounds easy. Right?
So give it a try.
Before reading the rest of this article, take a pencil and a sheet of paper and try to find the solution.
Have fun with the digits!
Elegant or brute force
Maybe, you are a math genius and you are able to find the elegant solution to this riddle and to prove mathematically that your solution is correct.
It’s not my case, so we are going to go with a brute force algorithm.
We are going to go over the 6!
permutations and take the one that leads to the greatest number.
But, wait a minute 6!=720
!
How are we going to generate those 720 permutations?
Hmm….
StackOverflow to the rescue
Let’s import a piece of javascript code from a gist for generating the permutations of an array:
For instance, let’s see all the permutations of [1, 2, 3]
:
permutations([1,2,3])
By the way, all the code snippets of this page are live and interactive powered by the klipse plugin:
 Live: The code is executed in your browser
 Interactive: You can modify the code and it is evaluated as you type
StackOverflow to the rescue  again
We will need another convenient function maxBy
that calculates the element of an array that maximizes a function.
Again, let’s import a piece of javascript code from a gist for maxBy
:
Let’s see maxBy
in actions:
maxBy(function(s) { return s.length;}, ['albatross', 'dog', 'horse'])
The brute force algorithm
Our algorithm is going to be very straightforward:

Generate all the permutations of
[1,2,3,4,5,6]

Take the permutation
[a,b,c,d,e,f]
such thatabc*de*f
is maximal
Let’s write it in a single line of javascript code, using maxBy
, permutations
and EcmaScript 6 destructuring:
maxBy(([a,b,c,d,e,f]) => (100*a+10*b+c) * (10*d+e) * f, permutations([1,2,3,4,5,6]))
As you can see, the best permutation is:
431*52*6
PS: Do you have a more elegant solution to this riddle? Let us know in the comments below…