Permutation question (i think): combination of 25 numbers which ascend but never rep

Let's say i have the numbers 1 to 100

Within the range of these numbers there is a combination of 25 numbers which ascend but never repeat.

For example: 2, 4, 5, 10, 15... And so on.

is it possible to find the correct combination using a computer? How long would it take?

Thanks.

Goobas said:

Let's say i have the numbers 1 to 100

Within the range of these numbers there is a combination of 25 numbers which ascend but never repeat.

For example: 2, 4, 5, 10, 15... And so on.

is it possible to find the correct combination using a computer? How long would it take?

Click to expand...

I'm sorry, but I'm not quite understanding your question. Please reply with the full and exact text of the exercise, the complete instructions, and a clear listing of your thoughts and efforts so far. Thank you!

stapel said:

I'm sorry, but I'm not quite understanding your question. Please reply with the full and exact text of the exercise, the complete instructions, and a clear listing of your thoughts and efforts so far. Thank you!

Click to expand...

I'll try.

As far as i know, my question is some sort of permutation.

The number of items i have to choose from is 100 (n=100)

The number of items i'm going to choose from that pool is 25 (r=25)

The order of the items matter and they cannot repeat. The difference being that the order of the items are chosen in an ascending manner.

let's say there are 100 people lined up, each with an assigned number, ranging from 1 to 100, all in ascending order ready to be chosen for a sports game. The person picking players walks past all 100 people while choosing 25 players to play in the game, all at random, but in ascending order. Maybe he picks player 3, 5, 9... 50, 54, 58... And so on.

Is it possible for a computer to guess the correct order chosen, just by brute forcing each possible order? If so, how long would it take?

Goobas said:

The number of items i have to choose from is 100 (n=100)

The number of items i'm going to choose from that pool is 25 (r=25)

The order of the items matter and they cannot repeat. The difference being that the order of the items are chosen in an ascending manner.

let's say there are 100 people lined up, each with an assigned number, ranging from 1 to 100, all in ascending order ready to be chosen for a sports game. The person picking players walks past all 100 people while choosing 25 players to play in the game, all at random, but in ascending order. Maybe he picks player 3, 5, 9... 50, 54, 58... And so on.

Is it possible for a computer to guess the correct order chosen, just by brute forcing each possible order? If so, how long would it take?

Click to expand...

You haven't said what makes one choice "correct". Perhaps you are asking this: if one set of 25 is considered correct (e.g. by being the combination that would let you open a door), how many different choices are there, that a computer would have to try in searching for the "correct" one? This might determine how long it would take to find it by just trying every one, and therefore whether it is feasible. (You'd need to know more than you've told us in order to actually say how long it would take.)

Do you recognize that this is actually a combination problem, not permutations? Since the order must be increasing, every possible subset of the 100 counts only once; you aren't counting different orders of choosing as different, since you are only allowing one such order. If you have learned the formula for combinations (or have a calculator that can do it), you can find the answer quickly. (You'll find that it is, indeed, a large number.)

Now, you were asked to quote the entire problem exactly as given to you, and what you wrote still doesn't sound like that. Is this a problem from a textbook or class, or something else? It can be important for us to know the source of a question, and the context in which you ask it (e.g. how much do you know about combinations and permutations?).

Dr.Peterson said:

You haven't said what makes one choice "correct". Perhaps you are asking this: if one set of 25 is considered correct (e.g. by being the combination that would let you open a door), how many different choices are there, that a computer would have to try in searching for the "correct" one? This might determine how long it would take to find it by just trying every one, and therefore whether it is feasible. (You'd need to know more than you've told us in order to actually say how long it would take.)

Click to expand...

Yes, that's what i'm asking, how many different combinations (aproximately) that would be needed to let you open a door, given the rules specified.

I understand that it's impossible to give the exact time it would take to find the correct combination, as luck is involved, but i was wondering if the number is large enough to make the average time to find the combination 10+ years.