----------------------------------------------------------------------------- -- | -- Module : Data.SBV.Examples.Puzzles.DogCatMouse -- Copyright : (c) Levent Erkok -- License : BSD3 -- Maintainer : erkokl@gmail.com -- Stability : experimental -- Portability : portable -- -- Puzzle: -- Spend exactly 100 dollars and buy exactly 100 animals. -- Dogs cost 15 dollars, cats cost 1 dollar, and mice cost 25 cents each. -- You have to buy at least one of each. -- How many of each should you buy? ----------------------------------------------------------------------------- module Data.SBV.Examples.Puzzles.DogCatMouse where import Data.SBV -- | Use 16-bit words to represent the counts, much larger than we actually need, but no harm. type Count = SWord16 -- | Codes the puzzle statement, more or less directly using SBV. puzzle :: Count -> Count -> Count -> SBool puzzle dog cat mouse = dog .>= 1 &&& dog .<= 98 -- at least one dog and at most 98 &&& cat .>= 1 &&& cat .<= 98 -- ditto for cats &&& mouse .>= 1 &&& mouse .<= 98 -- ditto for mice &&& dog + cat + mouse .== 100 -- buy precisely 100 animals &&& 1500 * dog + 100 * cat + 25 * mouse .== 10000 -- spend exactly 100 dollars (use cents since we don't have fractions) -- | prints the only solution: -- -- @ -- dog = 3 :: SWord16 -- cat = 41 :: SWord16 -- mouse = 56 :: SWord16 -- @ solve :: IO () solve = print =<< allSat (forAll ["dog", "cat", "mouse"] puzzle)