192 UNICUBSAL PROBLEMS [CH. IX 



extended before it could be applied to these solids. I offer 

 the suggestion to anyone who is desirous of inventing a new 

 game. 



Another and a very elegant solution of the Hamiltonian 

 dodecahedron problem has been given by M. Herniary. It 

 consists in unfolding the dodecahedron into its twelve penta- 

 gons, each of which is attached to the preceding one by only 

 one of its sides; but the solution is geometrical, and not 

 directly applicable to more complicated solids. 



Hamilton suggested as another problem to start from any 

 town, to go to certain specified towns in an assigned order, 

 then to go to every other town once and only once, and to end 

 the journey at some giv« a town. He also suggested the con- 

 sideration of the way in which a certain number of towns 

 should be blocked so that there was no passage through them, 

 in order to produce certain effects. These problems have not, 

 so far as I know, been subjected to mathematical analysis. 



The problem of the knight's path on a chess-board is some- 

 what similar in character to the Hamiltonian game. This I 

 have already discussed in chapter VI. 



