Last week’s Micro Softy was difficult because it involves graph theory. You’ll find the solution below. But first, here’s this week’s puzzle:

We are back in 1955 when train tickets were cheap. There was a long lineup at the ticket window at Grand Central Station. The ticket seller, who was blind, sold tickets from his booth with minimum talk.

Claire was the next in line to buy tickets. The ticket seller asked “Where to?” and Claire responded “Going to Piscataway.” The ticket seller said “That’ll be 40 cents.”  Claire gave him a dollar. Without saying another word, the blind ticket teller took the money and handed Claire two tickets and 20 cents change.   Claire thanked him and walked to the platform to board with Tom, her twin brother, who was a mute.

This week’s Micro Softy question: There was no other communication with the blind ticket seller. So how did he know that Claire wanted to buy two tickets?

This is a fascinating puzzle with an obvious solution.

Solution to Micro Softy 13: Garbage Trucks, String Theory and Stained-Glass Windows

Last week’s Micro Softy challenged puzzlers to bend a string along a path without the string overlapping itself.

The solution for the first three paths from last week is shown in Figure 1. The puzzles are shown on the left and the solutions are on the right, outlined in red:

The second part of the puzzle is more difficult. A stained-glass window has its colored panes separated by a lead strip called a came.  Can a single long came be bent with no overlaps to be the border of the stained-glass window shown on the left in Figure 2? The answer is yes. With no overlap, a solution is given on the right:

If you can code, this problem can be solved on a computer. My first approach would be a tree search.

Here are the puzzles from the last two Mondays: Micro Softy 12: Can You Connect the Dots? You may use no more than four perfectly straight lines and the lines must be connected. This classic puzzle in simple graph theory resulted in a commonly used phrase. Can you guess it?

Micro Softy 13: Garbage Trucks, String Theory… … and Stained-Glass Windows. What connects them? These puzzles, associated with the great mathematician Leonard Euler (1707‒1783), have a practical use, for example, in laying water pipes.

Note: At Monday Micro Softy 11: What Happened to That Other Dollar?, you will also find links to the first ten Micro Softies. Have fun!