MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2016 Latvia Baltic Way TST
1
1
Part of
2016 Latvia Baltic Way TST
Problems
(1)
delete 2 numbers from 1/2016 - 2/2016 and replace them with 3ab - 2a - 2b + 2
Source: 2016 Latvia BW TST P1
12/17/2022
2016
2016
2016
numbers written on the board:
1
2016
,
2
2016
,
3
2016
,
.
.
.
,
2016
2016
\frac{1}{2016}, \frac{2}{2016}, \frac{3}{2016}, ..., \frac{2016}{2016}
2016
1
,
2016
2
,
2016
3
,
...
,
2016
2016
. In one move, it is allowed to choose any two numbers
a
a
a
and
b
b
b
written on the board, delete them, and write the number
3
a
b
−
2
a
−
2
b
+
2
3ab - 2a - 2b + 2
3
ab
−
2
a
−
2
b
+
2
instead. Determine what number will remain written on the board after
2015
2015
2015
moves.
combinatorics