Three utilities problem
（重定向自Utility graph）
![The utility graph, also known as the Thomsen graph or K3,3](/Images/godic/202502/19/Biclique_K_3_3.svg1625.png")
![K3,3 drawn with only one crossing.](/Images/godic/202502/19/K33_one_crossing.svg1625.png")
The classical mathematical puzzle known as the three utilities problem; the three cottages problem or sometimes water, gas and electricity can be stated as follows:
The problem is an abstract mathematical puzzle which imposes constraints that would not exist in a practical engineering situation.