2021 AMC 12A Problems/Problem 25

Problem

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Start off with the number 1. Multiply 1 by 2. When you multiply 1 by 2, you double the number of divisors and you divide it by $\sqrt[3]{2}$ . Multiply 2 by 2. When you multiply 2 by 2, you triple and then halve the number of divisors. You must not forget to divide it by $\sqrt[3]{2}$ again to get that function. Keep up multiplying by 2 until it starts to decrease. Keep on multiplying by 3 until it starts to decrease. Keep on multiplying by 5 until it starts to decrease. Keep on multiplying by 7 until it starts to decrease. You cannot multiply by 11 because first multiplication automatically causes a decrease. $1 \rightarrow 2 \rightarrow 2^2 \rightarrow 2^3 \rightarrow 2^33 \rightarrow 2^32^2 \rightarrow 2^33^25 \rightarrow2^33^257$ This is like the computer science algorithms. ~Lopkiloinm

Note

See problem 1.

2021 AMC 12A (Problems • Answer Key • Resources)
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All AMC 12 Problems and Solutions

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2021 AMC 12A Problems/Problem 25

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Problem

Solution

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