A quick maths question

[ClaudiaWankleman]

I'm trying to do this calculation on my phone and it just isn't working for me - can someone give me an answer (and possible a formula to work this out in the future?)

If I have 10 people doing activities, and would like everyone to work with everyone else in a 2 person partnership, what is the fewest amount of activities required to be scheduled?

I'm not sure whether I've understood your question, but are you asking how many pairs you can have if everyone has to work with someone different at least once for this event?

Each person needs to work with 9 other people - so nine?

Or am I misunderstanding you.

Yes sorry - I read that back and I didn't explain well.

I want to organise various 'activity stations' and have each attendee work with every other attendee once. If there are 10 people attending, how many activities do I need?

That's if you don't want anyone to repeat an activity.

45 activities.

The first person has to do 9 activities so they do something with everyone. The next person 8 (as they’ve already done one with the first person). Then 7, 6, 5 and so on.

So the maths is:

9+8+7+6+5+4+3+2+1=45

Or...

(9x10)/2 = 45

Wiseowl has got it. Just use the triangular number formula n(n+1)/2 to find the number of pairs for n people.

But that's not 45 different activities, that's 9 activities over 5 sessions.

So 9.

Not over 5 sessions, but with 5 groups of two people.

Thanks all.

I had worked out the 45 but I knew it was combinations, not actual activities.

The number of actual activities required should always be one less than the number of participants I have (right)?

Yes, unless you are happy for people to repeat activities.

@WiseOwl69

45 activities.

The first person has to do 9 activities so they do something with everyone. The next person 8 (as they’ve already done one with the first person). Then 7, 6, 5 and so on.

So the maths is:

9+8+7+6+5+4+3+2+1=45

Or...

(9x10)/2 = 45

That's individual activity events; if you are setting up stalls and having everyone work at one at a time, so everyone working simultaneously, then move round, you would need at 5 (and everyone people will do at least one activity twice). But you will need 9 "rounds" of activities to get everyone done.

Do you want each pair to do the same activity repeatedly or do a range of activities and work with different people? Because I think that matters to the answer and how many stations you need.

Eg person 1 plays cards. They play cards with persons 2 to 10. Do you also want person 2 to play cards with person 3 etc, or do you want person 2 to play dominos with persons 1 and 3 to 10?

I think the answer is 5 or 9, but I've already deleted one post trying to explain why, because it got really complicated.

As you have worded the question it would be 1 activity, and then 45 repeats of it.

As I think you want it, it is probably 9 as each person needs to work with 9 others, and I think you want them to not repeat activities. (I say think as I haven't checked you could achieve this perfectly with no one having to wait around.)

(Or, you could have 45 activities, so each activity is only done once.)