The Missing Data Page: A Sunday Geometry Trick

In this missing data page puzzle, two arrangements seem to make the same triangle. Why does the second show a gap?

This picture is a small cousin of the classic missing-square puzzle. It looks like two large right triangles sitting on identical grids. In the lower drawing a white square opens up. No card was stolen from the desk, and the printer did not skip a page.

Look closely at the long diagonal edge in each arrangement. The red wedge rises three grid units over a run of eight. The teal wedge rises two over five. Those are close slopes, but they are not equal. In one arrangement the join bends one way; when the wedges change order, the join bends the other way. The grid makes the bend easy to miss.

Before you scroll, decide what you think the yellow region represents. Is it a third fixed puzzle piece, or is it simply the area left under the apparent diagonal? That question is the key to the trick shown here.

The Missing Data Page Answer

The yellow is remaining area, not a fixed piece. Only the red and teal wedges have been moved. Their slopes are 3/8 and 2/5. In decimals, that is 0.375 and 0.4. Because those numbers differ, the broken diagonal is not one straight line. The two outlines are not the same triangle, even though the grid invites you to read them that way.

The white cell in the lower picture is paid for by a thin change in area along the bent edge. Nothing appears from nowhere. The colours are honest; the quick assumption that both outlines are identical is the part that fails.

I enjoy this one because the error is so small and so persuasive. We often see a straight-looking line, a round-looking number or an almost-matching total and stop checking. A grid does not guarantee that our eye has measured the geometry correctly.

No SQL Server engine is involved in this drawing. The database connection is the habit it teaches: when a count feels impossible, name the assumption and measure it. I would rather discover a tiny slope difference in a Sunday picture than a missing row in a Monday report.

Published by Pinal Dave on SQLAuthority. More of my work at pinaldave.com.