A and E are the first two, and X and Y are the
last two letters of the alphabet which can't be
drawn without lifting the pencil.
In a pencil or pen drawing, if some straight or curved lines
meet at a point, or ends at a single point, that point is
called a "vertex" (plural "vertices"), or "node".
If the number of straight or curved lines meeting at a vertex
is even, we say the vertex is even, and if that number is odd,
we say the vertex is odd. If a straight or curved line ends at
a point, we say that point is odd since only one line issues
from that point, and 1 is an odd number.
These capital letters in simplest form:
B, C, D, I, J, L, M, N, O, P, R, S, U, V, W, Z
can all be drawn without lifting the pencil or retracing.
because each has no more than 2 odd vertices in the simplest
way to. That's because any pencil or pen drawing which can
be drawn without lifting the pencil or pen or retracing must
have 1 beginning and 1 end. That's 2, and no more!
These can't be drawn without lifting or retracing:
A, E, F, G, H, K, Q, T, X, Y
Here is an example of one letter, A, that cannot be drawn without
taking up the pen or pencil or retracing, and one letter, P, which
can be. The odd vertices are indicated with a red circle and the
even ones with a green circle. The A has 4 odd vertices and 1
even vertex. So it can't be drawn without lifting the pen or pencil
or retracing, because it has more than 2 odd vertices. However
The P has 1 even vertex and 2 odd vertices, so it can be drawn
without lifting the pen or pencil or retracing.
But, again, the answer to your problem is A,E, and X,Y.
Edwin
