Happy Little trees 🌲🌲🌲

Number Theory Level 3

A forest has a relationship between the numbers of trees and camps. To find the number of trees, T T , you use the 🌲 operator, which multiplies the factors of the number of camps, C C , together. For example,
50 🌲 = 1 × 2 × 5 × 10 × 25 × 50 = 125000 . 50🌲 = 1 \times 2 \times 5 \times 10 \times 25 \times 50 = \boxed{125000}. How many camps are there if there are 3111696 trees?


The answer is 42.

Brack Harmon by Brack harmon , 18, USA

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2 solutions

Giorgos K.
Mar 19, 2018

Mathematica

n=1;While[Times@@Divisors[n++]!=3111696];n-1

returns the answer to the meaning of life, the universe, and everything.

42 42

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Brack Harmon
Mar 18, 2018

C C 🌲 = C C ^# of factors / 2

using our example, 50🌲= 5 0 3 50^3

Thus, we find the n n roots of 3111696

3111696 \sqrt{3111696} = 1764

3111696 3 \sqrt[3]{3111696} = 145.99...

3111696 4 \sqrt[4]{3111696} = 42

...

1764 🌲 ≠ 3111696

42 🌲 = 3111696

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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