Question

Chloe made a conjecture that given any two numbers the greater number can always be arranged into more arrays state weather you agree or disagree then explain why you think so by giving an example of two numbers that prove or disprove the conjecture

Answer 1

I disagree with Chloe's conjecture.

To disprove the conjecture, I can give an example of two numbers that do not follow this rule. Let's consider the numbers 5 and 3. Here are all the possible arrays for these numbers:

For 5: {5}, {1, 1, 1, 1, 1}, {1, 2, 2}, {1, 4}, {5}
For 3: {3}, {1, 1, 1}, {1, 2}, {3}

As we can see, the number 5 can be arranged into more arrays (5 arrays in total) than the number 3 (4 arrays in total). Therefore, this counterexample disproves Chloe's conjecture.