# Brainteasers Answers — Issue 30, 2014

In each issue of the Automation Notebook we feature a section of brainteasers. These are the brainteaser answers from Issue 30, 2014 of Automation Notebook. The brainteaser questions are repeated in black. The answers to the brainteaser questions are highlighted in red with explanations. You can view the brainteasers from Issue 30, 2014 without the answers here.

Fractional Shipping

The harried shipping clerk at the puzzle factory knew he had shipped just over 20,000 puzzles for the week, but he had lost track of the actual numbers.  He did recall that one-third of Mondays shipping total, two-sevenths of the Tuesday total, seven-twelfths of the Wednesday total, nine-thirteenths of the Thursday total, and fifteen-twenty-seconds of the Friday total were all the exact same (whole)number of puzzles.  Can you determine the total number of puzzles shipped that week?

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## Cubic Unfolding

Cutting a cubical box along seven (and only seven!) edges allows the sides to open to a flat shape such as the two shown below. Not counting the versions that are merely reflections or rotations of others, how many unique shapes can be formed?

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## Fold the Sheet

Make a 2×4 rectangle out of paper, and write the numbers 1-8 on it as shown. Can you fold the paper into a 1×1 flat stack so that the numbered panels are in order from 1 to 8 through the stack, with the “1” on top and facing outward? No tearing is required, just folding and bending.

Answer: We almost gotcha on this one. To put this solution into words or produce some kind of flat imagery, would probably have been confusing. So instead, we made a quick video for you to see the solution.