ĐỀ THI TOÁN APMO (CHÂU Á THÁI BÌNH DƯƠNG) ĐỀ 33 pot
ĐỀ THI TOÁN APMO (CHÂU Á THÁI BÌNH DƯƠNG)_ĐỀ 33 pot
... from its two neighbours
A
i−1
and A
i+1
. (Here A
n+1
means A
1
and A
n
means A
0
.) How should this redistribution be
performed so that the total number of objects transferred is minimum?
ĐỀ THI TOÁN APMO (CHÂU Á THÁI BÌNH DƯƠNG)_ĐỀ 12 pot
... < 180
◦
−
(
∠B + ∠C
2
)
= 90 +
∠A
2
< 120
◦
.
In this way, a special case of the problem can be easily proved.
2
again by induction hypothesis. Combining (†), (‡) and
f(2
k
− 1) = f(2(2
k−1
− ... we obtain
a
k
= 2a
k−1
+ 2
k−1
− 1
for all k ≥ 3. Note that this recursive formula for a
k
also holds for k ≥ 0, 1 and 2. Unwinding
this recursive formula, we finally get
a
k
= 2a
k−1
+ 2
k−1
−...
