330 Answersform a true rectangle, then there is a long diamond-shaped space in the
middle uncovered, as in the diagram. This space is exactly equal in area to
one of the little square cells. Therefore we must deduct one from 65 to get 64
as the actual area covered. The size of the diamond-shaped piece has been
exaggerated to make it quite clear to the eye of the reader.
[For a discussion of many new and closely related paradoxes of this type,
see the two chapters on "Geometrical Vanishes" in my Mathematics, Magic,
and Mystery (Dover, 1956, pp. 114-155).-M. G.]- PROBLEM OF THE MISSING CELL
The diagram shows how the four pieces may be put together in a different
way, so that, on first sight, it may appear that we have lost a cell, there now....... ......
...... ......
~
.....
r--...
...... ....being only sixty-three of these. The explanation, as in the case of the preced-
ing fallacy, lies in the fact that the lines formed by the slanting cuts do not
coincide in direction. In the case of the fallacy shown in the puzzle here, if
the pieces are so replaced that the outside edges form a true rectangle, there