Marcus L. Rowland (ffutures) wrote,
Marcus L. Rowland
ffutures

logic puzzle

On Friday, for a school science lesson on acids, I printed sets of five labels, one of each of the following names on a single 38 x 98mm printer label, and cut them apart afterwards. They were all the same width, the same font and point size was used throughout.

Soap
Vinegar
Water
Baking Soda
Lemon

I prepared 8 labelled beakers of each of those solutions, all the same size beaker.

After the lesson I threw away the solutions and loaded a dish washer with the 40 labelled beakers, all of which had contained one of the chemicals - and yes, there were still 8 of each.

The beakers were put into the machine randomly, because I was in a rush I didn't remove the labels first - they usually wash off and can be removed from the filter in the machine fairly easily.

This morning 33 out of 40 beakers were missing the labels. 6 out of the 7 that still held labels had held baking soda.

There is a simple explanation as to why this happened. Can you guess it before looking behind the cut?



I printed the labels across the NARROW width of the paper, so that they came out in strips 38mm wide. Because I wanted them readable I used a large font.

Baking soda is the longest name and is two words, and came out as two lines of text. All of the others were a single word. When I cut them apart, the baking soda labels had twice the area of paper, but only 25% more edge.

The efficiency with which labels are washed off is probably inversely proportional to the ratio of the size of the label to the length of the edge. The bigger the label, the smaller the edge in proportion, and the less likely it is to be washed off.

There's probably a research paper for someone in this...

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