Mathematics for Computer Science

“mcs” — 2017/3/3 — 11:21 — page 618 — #626
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Chapter 15
Cardinality Rules
2. The suit of the extra card, which can be selected in 4 ways.
3. The rank of the extra card, which can be selected in 12 ways.
For example, the hand above is described by the sequence:
.7; K; A; 2; }; 3/ $ f7}; K|; A~; 2; 3}g:
Are there other sequences that correspond to the same hand? There is one more!
We could equally well regard either the 3} or the 7} as the extra card, so this
is actually a 2-to-1 mapping. Here are the two sequences corresponding to the
example hand:
.7; K; A; 2; }; 3/ &
.3; K; A; 2; }; 7/ %
f7}; K|; A~; 2; 3}g
Therefore, the number of hands with every suit is:
13 4 4 12
:
2
15.8 The Pigeonhole Principle
Here is an old puzzle:
A drawer in a dark room contains red socks, green socks, and blue
socks. How many socks must you withdraw to be sure that you have a
matching pair?
For example, picking out three socks is not enough; you might end up with one
red, one green, and one blue. The solution relies on the
Pigeonhole Principle
If there are more pigeons than holes they occupy, then at least two
pigeons must be in the same hole.