三，再来一次
Tri, Tri Again
题目详情
Label the sides of a tetrahedron with 1, 17, 71, and 711. On the board presented here, place the tetrahedron on one of the top 8 triangles, and roll it until it reaches one of the bottom 8 triangles, such that whenever the tetrahedron is touching the board (including its initial placement), the number on its base equals the number on the board. What is the lowest possible sum of numbers that your tetrahedron encounters?
解析
Original Explanation
As it turns out there are very few paths the tetrahedron can take from top to bottom, and the shortest/cheapest one is presented here. The sum of the numbers the tetrahedron rolls over on its path is 7252.
Astute solvers noticed that for a tetrahedron with sides A, B, C, and D, when it rolls in a “straight line” (such as moves 2 thru 5 in this solution), the faces on the paper form the pattern ABCDABCD…, and when it begins to roll in a “circle” (such as the one begun by moves 1 thru 4 in this solution), the faces on the paper form the pattern ABCABCABC… . From there, one can logically deduce the path the tetrahedron must take.
Congratulations to everyone who solved this month’s puzzle!