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Contests
National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
1980 Swedish Mathematical Competition
5
5
Part of
1980 Swedish Mathematical Competition
Problems
(1)
no of words with 12 letters constructed by 2 symbols
Source: 1980 Swedish Mathematical Competition p5
3/28/2021
A word is a string of the symbols
a
,
b
a, b
a
,
b
which can be formed by repeated application of the following: (1)
a
b
ab
ab
is a word; (2) if
X
X
X
and
Y
Y
Y
are words, then so is
X
Y
XY
X
Y
; (3) if
X
X
X
is a word, then so is
a
X
b
aXb
a
X
b
. How many words have
12
12
12
letters?
combinatorics
Words