Issue 46, 2021Notebook Issue

Brainteasers – Issue 46, 2021

Zig or Zag

The factory manager wants to know how many routes there are for the AGV (Automated Guided Vehicle) in the lower left corner to get to the charging station in the upper right (see the diagram below).  The AGV must always travel along the lines shown such that it gets closer to the charging station with each move; that is, it must always travel either North, East, or Northeast along the lines.

Dividing Fluid

The factory manager purchased a barrel containing 24 liters of cutting fluid for the factory’s three CNC machines.  She desires that the fluid be divided evenly between the three machines – but the only buckets available hold 5, 11, and 13 liters respectively.  How do the machine operators divvy up the cutting fluid?  What is the minimum number of pouring operations possible to arrive at three containers with exactly 8 liters in each?

Diagon Allie

The factory floor contains 64 work cells alternately painted blue and white as shown.  Starting in the upper left work cell, Allie (the AGV) needs to visit all the white work cells, without fully entering ANY of the blue cells (she will always move diagonally).  And she must not cross any of the intersections more than once.  It can be done with 17 straight segments.  Can you find Allie’s path?

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Brainteaser Answers

Zig or Zag

Starting in the lower left corner consider how many ways there are to get to each vertex, and label that vertex with the number of possibilities.  Work your way up and to the right, adding the number of possibilities from the connecting vertices as you move through the entire matrix.  As shown below, the final number of possibilities to reach the upper right corner (at the charging station) is 321 routes.

Slippery Division

Start with 24 liters in the original container – use it to fill the 11 and the 5 liter buckets, leaving exactly 8 liters in the original.  Empty the full 11 liter bucket into the 13 liter bucket.  From the full 5 liter bucket, finish filling the 13 (which takes 2 liters, and pour the remaining 3 liters into the 11 liter bucket.  Then fill the 5 liter from the 13 liter bucket – leaving exactly 8 liters in the 13 liter bucket, then pour the full 5 liter bucket into the 11 liter (contains 3 liters prior to this pour) to make 8 liters in the 11 liter bucket.  The qualities in the containers after each pour are shown below.

Container Size:         24        13        11        5

Start                            24        0          0          0

1st pour                        8          0          11        5

2nd pour                       8          11        0          5

3rd pour                        8          13        3          0

4th pour                        8          8          3          5

5th pour                        8          8          8          0

Diagon Allie

A path with 17 legs is shown below.  There are several variations, and mirror image solutions.  Can you do it with fewer segments?  Drop us a line at  Please include “Brainteaser August 2021” in the title, and your complete mailing address.  We would love to see your solution!