MathDB

Let

n

be a positive integer. On a number line, Azer is at point

0

in his car which have fuel capacity of

2^n

units and is initially full. At each positive integer

m

, there is a gas station. Azer only moves to the right with constant speed and doesn't stop anywhere except the gas stations. Each time his car moves to the right by some amount, its fuel decreases by the same amount. Azer may choose to stop at a gas station or pass it.
There are thieves at some gas stations. (A station may have multiple thieves) If Azer stops at a station which have

k\ge 0

thieves while its car have fuel capacity

d

, his cars new fuel capacity becomes

\frac{d}{2^k}

. After that, Azer fulls his cars tank and leaves the station. Find the minimum number of thieves needed to guarantee that Azer will eventually run out of fuel.
Proposed by Mehmet Can Baştemir and Deniz Can Karaçelebi

Problem Statement