Maths Olympiad Prep

Track / Stage 4 / 140 of 340 #400 of 1964

Problem 400

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

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. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

1920\begin{array}{l} 19 \\ \hline 20 \\ \hline \end{array}

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.