Maths Olympiad Prep

Track / Stage 4 / 128 of 340 #388 of 1964

Problem 388

AMC 12 late, AIME early
Combinatorics Difficulty 4.8 Find the answer

19. Zhu Bajie picked a bag of wild fruits on the mountain and brought it back to Tang僧. While walking, he got hungry, took out half of them, hesitated, put back two, and then ate them. While walking, he got hungry again, took out half of them, put back two, and then ate them. He did this four times, taking out half and putting back two each time. When he finally returned to Tang僧, there were 5 wild fruits left in the bag. Originally, Bajie picked \qquad wild fruits.

A number or a short expression. Spacing and $ signs are ignored.

Official solution

\begin{tabular}{l}
19 \\
\hline 20 \\
\hline
\end{tabular}

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.