Lesson 5

It is easy to see that the numbers break into independent chains, in each of which no more than one of the two neighboring numbers can be taken. For example, \[3, 6, 12, 24, 48 \ .\] Thus, from a chain of length \(k\), at most \(\lceil \frac{k}{2} \rceil\) elements can be taken (this is the number \(k/2\) rounded up): you need to take every second element, starting from the first. In total, 33 elements will be collected. Below are the chains, with the elements that should be taken highlighted. The shown solution is not the only one: for example, from the first chain, you could take the elements \(2, 8, 32\).