A little brain exercise

November 20th, 2007

”Practice doesn’t make perfect. Perfect practice makes perfect.” – Vince Lombardi

Here’s a cool logic problem that a friend shared recently:

There are 14 cards on a table. Each card can be numbered with a number 1 through 10. Each three consecutive cards must sum to 18. The fourth card is a 7, and the twelfth card is an 8. What is the eighth card?

I had problems reasoning it out, so I decided Ruby would save the day! So I wrote some code to try a brute force search, and here’s what I came up with:

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#!/usr/bin/ruby
O = [nil, nil, nil, 7, nil,
     nil, nil, nil, nil, nil,
     nil, 8, nil, nil];

def checker(arr)
    (0..(arr.length-3)).each do |i|
        return false if (arr[i].nil? or arr[i+1].nil? or arr[i+2].nil?)
        if ((arr[i] + arr[i+1] + arr[i+2]) != 18) then
            return false
        end
    end
    return true
end


k = O.clone
(0..(k.length-1)).each do |i|
    k[i] = 1 if k[i].nil?
end

stop = false
MAX = 10
p = 0
cnt = 1

while (!checker(k)) do
    cnt += 1
    while k[p] == MAX do
        k[p] = 1
        p += 1
        while (O[p] != nil) do
            p += 1
        end
    end

    k[p] += 1
    p = 0
end

puts k.join(" ")

Feeling quite satisfied with myself, I set my machine into motion. Then I added some puts trace statements to see how quickly I could expect my answer. Finally, the reality of the situation came into focus, as rough estimates showed me that it would take about 400 hours to arrive at the answer with this code running on my setup.

Sure it could be tweaked to use heuristics of the problem to search more efficiently, but the point of my idea was to try and be lazy and let Ruby do all the work. I even tried a random search before the current version of the code, that wasn’t happening either. Although imagine how crazy it would have been if it did! Sometimes it’s easy to underestimate a problem.

Anyway, after revisiting the problem and just applying some simple logic, the answer came pretty quickly. Sometimes it’s also easy to overestimate a problem.

Posted by rboyd Filed in

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