i have to make a conjecture on if there is more or less than 50 numbers that can be written as product of 3 digit numbers w/o using the number 1 more than once as a factor. Example: 10 can be 1*2*5 and 24 can be 2*3*4

To clarify, are you saying that the have to be composed of three single digit numbers?

Also, if one number has more than one acceptable composition, is it counted once of multiple times towards the 50? For example, 24 could be 2*3*4 or it could be 8*3*1; does that count as 1 or 2 examples?

yes i think they all have to be single digit numbers. and the second thing is that it counts as two examples

I'm assuming you are not using zero or negative numbers as components.

So then you have to think of all the combinations of 3 of the 9 single number digits, where 1 can only be used once.

For example:
1*2*2
1*2*3
1*2*4
1*2*5
1*2*6
1*2*7
1*2*8
1*2*9

There's 8 possibilities already, and as you can see there are eight more for 1*3*X.

Therefore, it's safe to assume that there are many more than 50 possibilities.

It is way more.

Reasoning is as such:
a*b*c

a can be any number from 1-9
b can be any number from 2-9
c can be any number from 2-9
(because 1 can only be used once)

therefore, you are just multiplying the total possibilities available.

9 possible in a
8 possible in b
8 possible in c

9*8*8 = 576

i hope that helps you.

To make a conjecture on whether there are more or less than 50 numbers that can be written as a product of three-digit numbers without using the number 1 more than once as a factor, we can follow these steps:

1. Determine the possible three-digit numbers: Look for all the three-digit numbers that do not contain the digit 1. Count how many such numbers there are.

2. Calculate the total possible combinations: Since we can use each three-digit number more than once as a factor, we need to calculate the number of possible combinations. Multiply the number from step 1 by itself three times to account for each factor.

3. Evaluate if the number of combinations is greater than or less than 50: Compare the result from step 2 with the number 50. If the number of combinations is greater than 50, then the conjecture would be that there are more than 50 numbers. If it is less than 50, then the conjecture would be that there are fewer than 50 numbers.

Remember, this is just a conjecture based on the steps above. To obtain the exact answer, you would need to calculate the values in step 1 and step 2.