MathDB
Problems
Contests
International Contests
Tournament Of Towns
1995 Tournament Of Towns
(460) 5
(460) 5
Part of
1995 Tournament Of Towns
Problems
(1)
TOT 460 1995 Spring S A5 divide line segment [0,1] into BW segments
Source:
7/9/2024
(a) Divide the line segment
[
0
,
1
]
[0,1]
[
0
,
1
]
into smaller black and white segments so that, for any polynomial
p
(
x
)
p(x)
p
(
x
)
of degree no greater than two, the sum of increments of
p
(
x
)
p(x)
p
(
x
)
along all the black segments is equal to that along the white ones. (The increment of
p
(
x
)
p(x)
p
(
x
)
along the segment
[
a
,
n
]
[a, n]
[
a
,
n
]
is the number
p
(
b
)
ā
p
(
a
)
p(b) - p(a)
p
(
b
)
ā
p
(
a
)
.)(b) Can this be done for all polynomials of degree no greater than
1995
1995
1995
? (Burkov)
combinatorics
Coloring