Sum of 16 numbers out of 25, matching a number

Hello, alls.

I have attached an example file.

I have a serie of 25 various numbers (which can change). I would find all the combinations where 16 among them match a number (which can change).

Example :

The series of 25 numbers is : 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 - 16 - 17 - 18 - 19 - 20 - 25 - 30 - 35 - 40 - 50

5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20 (16 numbers) match 200

1+2+3+4+5+6+7+8+9+10+14+16+20+25+30+40 (16 numbers) match 200 as well.

Thanks for ny kind help.
Best.
Frederic

Hi,

Thanks for the kind answer.

Basically, it works well, but maybe I was not precise in my post, but :

- The 16 numbers must be chosen among those numbers of cells C2 to C26 (I can see other numbers in the results of your calculation).
- Those 16 numbers must be chosen once only (Sorry, this was not indicated in my post).
- The sum number (in Cell G5) can be modified.

Hope this will not need too much changes.
Thanks for the help.
Frederic

Yes, it works much better with your update.

The Point 2 means that if one number among the 25 possible choice (c2:c26) is chosen among the 16, it can be only chosen once.
So, this solution will match :

5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20 = 200, because each number appears only once.

but this solution will not match :

1+1+3+7+7+11+12+12+14+14+16+16+18+18+25+25 = 200, because there are several 1, 7, 12, 14, 16, 18, 25.

Also, if the sum number (200, in this example) can be variable ?

Thanks for all your time and skills.
Best.
Frederic

Thanks again, but is there any chance to solve the fact that all 16 values must be unique ?

Otherwise, it is useless. Let me explain :

The purpose of this calculation is destinated to see all posible combinations of money gains for a TV gameshow :

The sum of the 16 numbers (200 in the example) is the maximum winnings of the contestants.

The 25 possible numbers are each winnings per question (16 questions), but the winnings of each question must be different. This is why all values among the 16 must be unique.

Thanks if you can find any helpfull update.
Frederic

Hi.

Thanks. It works great. Of course, it takes time to calculate, but so far, 5 solutions have been found with 1 hour.

It helps much for the TV gameshow that I am designing for TF1, the French #1 channel and you can have the curiosity to see 1 min 30 of video of this gameshow's rehearsals in Paris here :

https://www.box.com/s/rfiedxye3a9xbat7kp9t

Have a nice day and thank you again.
Best.
Frederic