Programming Praxis – $7.11

Today’s Programming Praxis problem is an easy one.  We’re supposed to give the prices of four items, that both sum up and multiply to $7.11. Let’s get started.

While we could just do a brute force test on all possible combinations, this would take rather long. So in order to speed things up we only check numbers that are a proper divisor of $7.11.

divs :: [Int]
divs = [x | x <- [1..711], mod (711 * 10^6) x == 0]

Once we have the divisors, solving the problem becomes a fairly trivial list comprehension (the <= bits are another optimization to eliminate some identical combinations).

main :: IO ()
main = print [(a,b,c,d) | a <- divs,         b <- divs, b <= a,
                          c <- divs, c <= b, d <- divs, d <= c,
                          a + b + c + d == 711,
                          a * b * c * d == 711 * 10^6]

If we run this, we find there is only one combination that satisfies both requirements.