5

Part of 2023 LMT Spring

Problems(2)

2023 Spring LMT Team #5

Source:

How many ways are there to place the integers from

1

8

on the vertices of a regular octagon such that the sum of the numbers on any

4

vertices forming a rectangle is even? Rotations and reflections of the same arrangement are considered distinct

2023 LMT Spring Accuracy Problem 5

Source:

N = \sum^{512}_{i=0}i {512 \choose i}.

What is the greatest integer

a

2^a

is a divisor of

N