Probability

Hello,  This question may be a long shout, yet allow me to ask for your ideas and calculations.  It's for a worthy cause, so i hope you will not object to the question.  It is for www.rockymountaincfc.org/
This question is a fun question, do not spend very much time with it.
I'm setting up a fund raising project.  My objective is to raise at least $250.00, with a $50.00 prize.  
The attached Excel file has 30 clues which I would sell at $1.00 per clue.  I would at minimum get 50 employees to buy some clues.  At minimum each person will buy 1 clue, which is not enough to meet my goal.
50 employees would have to buy 6 clues maximum.  And the fewer the employees, the more they would have to buy.
And the more employees, the fewer each will need to buy.  At a 100, each need to buy 3.
Could you come up with a graph that would show the statistics?
Also, this is will be the way I will carry out the fund raiser. I will be hiding some figurines.  Each figurine will have a clue indicating its location. Each clue will have a multiplier (X1-X10).  Therefore, there will be 300 clues.  I will have these 300 clues in a box from which each buyer will pick the number of clues they purchase.  Whoever gets the highest multiple and finds the figurine from the clue will win.  If there is a tie, then I will have them draw the highest number from a hat, to pick the winner.  The prize I just learned is worth $60.00, so I would need at least 60 employees to buy a ticket.
From what I have written, do you foresee any possible conflicts/problems.
Probability.xlsx
chimaAsked:
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chimaAuthor Commented:
These are the rules;

The prize will be worth no less than $60
Each clue is sold for $1.00 each.
Clues will be picked from a box by the buyer.
The clues will be drawn during the lunch hour.
The first buyer will get to draw first, with the next buyer to follow, etc.
If a duplicate clue is drawn by a buyer, all of the clue’s multiplier will be counted.
The buyer with the highest number of figurines, with the highest added multiplier will be the winner.
If there is a tie, then their names (names will be duplicated 10 time each) will be thrown into a box and some other person will draw a name from the box.
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Thibault St john Cholmondeley-ffeatherstonehaugh the 2ndCommented:
I'm a bit confused over the rules. Are the purchased clues just available to help out if the clue on the figurine is not enough to find the next one?

It's a fund raiser for a good cause, I hope people would be pleased to give you $5 just to play. A treasure hunt with clues sounds great fun. If there was a $5 entry fee to get perhaps the first clue or a sheet of instructions then you only need 50 players and one clue bought each to reach your target.
You could add one location where you are only given the next clue if you can throw a coin into a bucket from 5 yards away, any that miss go straight into the charity pot.

Sounds great fun, good luck.
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chimaAuthor Commented:
Thibault,  thank you for your response.  My response to your questions are marked with >>>
I'm a bit confused over the rules. Are the purchased clues just available to help out if the clue on the figurine is not enough to find the next one?
>>> the purchase of the clues must cover the cost of the prize, and the amount given to the charity.  I hope the charity will get at least $200.00

It's a fund raiser for a good cause, I hope people would be pleased to give you $5 just to play. A treasure hunt with clues sounds great fun. If there was a $5 entry fee to get perhaps the first clue or a sheet of instructions then you only need 50 players and one clue bought each to reach your target.
>>> Correct, but I need to also make it "fun" for them to be encouraged to buy.
You could add one location where you are only given the next clue if you can throw a coin into a bucket from 5 yards away, any that miss go straight into the charity pot.
>>> This sounds like fun, but we are also limited in the time we can spend doing this.  At least the time needed to sell the clues.
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Thibault St john Cholmondeley-ffeatherstonehaugh the 2ndCommented:
>make it "fun" for them to be encouraged to buy.
I wasn't suggesting that they can't buy extra clues, just that an entry fee of a relatively small amount might help you reach your target faster.
It's not really a gamble, you want their money and you are selling entertainment. Grab what you can. Someone with a big wallet might buy 30 clues at stage one to ensure their win. They will be doing it to help the cause, but the effect could be that the prize is won before many have had a proper go and so won't buy the extra clues that you need to sell.
I've paid money for a sheet of questions before. The first one with all the correct answers won a prize, but the fun was in the questions and the money was already paid.
People will try to help for a good cause.
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nickg5Commented:
How many employees are there for you to sell clues to?
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chimaAuthor Commented:
Nickg5, I apologize for the delay.  I thought I would get to it over the weekend and i did not.  To answer your question; we are about 270 employees.  
Nickg5 please read my comment for Thibault, thanks

Thibault, These are the type of situations I want to have a discussion about; "Someone with a big wallet might buy 30 clues at stage one to ensure their win."  I want to avoid such problems.  Possibly I could place a limit on the number of clues that a single person can buy.  I also thought that if one clue had 5 or more multipliers and those clues (clue#1x1, clue#1x2, clue#1x3...etc, and clue#2x1, clue#2x2...etc, for a total of 300 clues in one box to draw from that this would prevent the buyer from hijacking the hunt.
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Thibault St john Cholmondeley-ffeatherstonehaugh the 2ndCommented:
You could limit the clues to one per player per level, but this could restrict your sales and you need to sell them. Some people will try to complete the exercise without buying any extra clues, mostly out of self pride, but possibly to try and win for the minimum cost.

I'm afraid I sound a bit slow to understand how the game works still.

Can you help me through a simple stage to show how the clues fit in?
I'm guessing I might start with a slip of paper with a clue on it, either purchased or given in return for entering.
I read the clue, it could be encrypted, but perhaps it says 'it might be hot and damp'.
I will rush off and hunt around the kitchen and the shower rooms.
I'm looking for a figurine but can't see one so I'll seek you out and ask to by an extra clue.
This clue hints to an empty coffee cup on the windowsill in the basement.
I find the figurine and a clue attached to it which I read and start to follow...

Is that close to how it works?
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nickg5Commented:
Hi,
There are 300 clues? How many clues does a smart puzzle solving person need to get the answer?

With 270 employees and if you have a good cause in the charity, it would seem that you might be able to get 25% of all employees to buy 1 ticket for $4. The 1 ($4) ticket for the 67 people gives you $208 for the charity and $60 for the prize.

If there are 300 clues and it is a scavenger hunt of sorts requiring lots of time and brain power, I might buy one clue.
That won't help you much but my decision is based on the complexity of the game.

In approaching 67 people for $4 the selling approach would be that not only will they help donate $208 to the charity but you will also have a drawing and a $60 prize will be awarded.

300 clues sounds like it will be hard to solve the puzzle. How many people will buy enough clues to have a chance of solving it. Can they win by buying 4 clues? If not it is less costly for them to just donate $4 and you only need 25% of the employees to participate at $4 and the company mail department could get a flyer out to all employees to advertise it.

If I was an employee and there were 300 clues, I'd really hesitate to give more than a couple or three dollars. I'd guess it will take half the clues to solve it and I am not going to invest $150.00.
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chimaAuthor Commented:
Thibault, "I'm afraid I sound a bit slow to understand how the game works still."  Your feelings/understanding are normal, because we (you and I, as we speak) are creating the game.  I have never seen a game like this, and I did not grab it from anywhere.  I thought of the idea and now I have to make it work.
One buyer/player will buy, for example 5 clues for 5 dollars.  He will draw the clues from a box holding 300 clues.  There are 150 (30*5) or I could have 300 (30*10), because each figurine will have 5 "copy" clues.  It is not that the 5 clues are different, it is that each clue has a multiplier written on it.  For example; clue#22: figurine located in the lab, X3.
A buyerA, picking 5 clues, could have picked; clue#22X4, clue#30x5, clue10x3, clue#4X2, and clue#22X5.  If no one else find those figurines, and buyerA finds them all, then his/her score is 19.  He/she has to be the highest to win.  Others could get to the same figurine, and buyerA will not find it, nor will his/her multiplier count.  Each buyer has to have both the figurine and the clue in order for the point to count.
One question is; If I get 100 employees to play, then I got to make the number of clue for it to work; should the clues be 150 of them, or should it be twice that; 300 clues?
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chimaAuthor Commented:
Nickg5, you are on the right frame of thinking.  I have to leave for the afternoon, but I like what you write, I'll read it closer tomorrow.
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nickg5Commented:
How many of the 300 clues will be needed to solve the puzzle?
That may tell you how many people will invest how many dollars in "x" number of clues.
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chimaAuthor Commented:
I had closed this ticket before.  I do not know why it did not get closed.
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nickg5Commented:
Good luck with your raffle or scavenger hunt.
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