+-----------------+ | C E | | | | | | D F | +---------------B | G | A | | | H | +-----------------+ ] As the conditions are generally understood, this puzzle is incapable of solution. This can be demonstrated quite easily. So we have to look for some catch or quibble in the statement of what we are asked to do. Now if you fold the paper and then push the point of your pencil down between the fold, you can with one stroke make the two lines CD and EF in our diagram. Then start at A, and describe the line ending at B. Finally put in the last line GH, and the thing is done strictly within the conditions, since folding the paper is not actually forbidden. Of course the lines are here left unjoined for the purpose of clearness. In the rubbing out form of the puzzle, first rub out A to B with a single finger in one stroke. Then rub out the line GH with one finger. Finally, rub out the remaining two vertical lines with two fingers at once! That is the old trick. 240.--THE UNION JACK. [Illustration: +-------+ +----- A B | | / \ | | / |\ \ | | / /| | \ \ | | / / | | \ \| |/ / | | \ | / / | | \ |\ /| / | +-----\-|-\/-|-/-----+ \| /\ |/ |/ \/ |\ /\ /| \/ |\ +-----/-|-/\-|-\-----+ | / / \| \ | | / | \ \ | | / /| |\ \ | | / / | | \ \ | |/ / | | \ \| / | | \ / | | \ -----+ +----- ] There are just sixteen points (all on the outside) where three roads may be said to join. These are called by mathematicians "odd nodes." There is a rule that tells us that in the case of a drawing like the present one, where there are sixteen odd nodes, it requires eight separate strokes or routes (that is, half as many as there are odd nodes) to complete it. As we have to produce as much as possible with only one of these eight strokes, it is clearly necessary to contrive that the seven strokes from odd node to odd node shall be as short as possible. Start at A and end at B, or go the reverse way. 241.--THE DISSECTED CIRCLE. [Illustration: