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Hanoi Open Mathematics Competition
2011 Hanoi Open Mathematics Competitions
9
function in N*xN*, f(x+1, y) = y[f(x, y)+f(x, y -1)], f(5, 5) (HOMC 2011 Q9)
function in N*xN*, f(x+1, y) = y[f(x, y)+f(x, y -1)], f(5, 5) (HOMC 2011 Q9)
Source:
July 25, 2019
function
two variables
positive integers
Problem Statement
For every pair of positive integers
(
x
,
y
)
(x, y)
(
x
,
y
)
we de fine
f
(
x
,
y
)
f(x,y)
f
(
x
,
y
)
as follows:
f
(
x
,
1
)
=
x
f(x,1) = x
f
(
x
,
1
)
=
x
f
(
x
,
y
)
=
0
f(x,y) = 0
f
(
x
,
y
)
=
0
if
y
>
x
y > x
y
>
x
f
(
x
+
1
,
y
)
=
y
[
f
(
x
,
y
)
+
f
(
x
,
y
ā
1
)
]
f(x +1,y) = y[f(x,y)+ f(x, y-1)]
f
(
x
+
1
,
y
)
=
y
[
f
(
x
,
y
)
+
f
(
x
,
y
ā
1
)]
Evaluate
f
(
5
,
5
)
f(5, 5)
f
(
5
,
5
)
.
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