By the way, guys, this is my second attempt of making a forum game. They show this on the TV show Countdown, the longest running game show in the world. OK: I have a selection of large numbers "25, 50, 75 and 100" and small numbers "1-10" and all you need to do is combine the numbers together to write a solution with the following numbers selected using the symbols +, -, * or / to reach the target number. Brackets are allowed as well.
I hope I explained clearly enough, if not here's an example:
Target number: 846
Selected numbers: 100, 50, 8, 4, 6, 10.
First you do 8*100 which is 800 then +50 which is 850 then -4 to the 850 which makes 846.
The solution can be written like this: 8*100+50-4
You haven't explained how this is going to work as a forum game. One person sets a puzzle, the next solves it and sets the next puzzle? If so, do you want to start, since it's your idea, and I'm sure the example puzzle wasn't meant to count?
No. So, we'll get the game started then!
I'll start with 1 large and 5 small numbers. And remember, hide your solutions and don't cheat using the solver please!
Target number: 376
75, 7, 5, 2, 4, 5.
Rather too easy:
75 x 5 + 5 - 4
Next puzzle:
97250, 6, 7, 4, 5, 3
I can do 963 so far.
EDIT: Got it! Quite hard though
50*5-7=243; 243*4=972
Next puzzle:
35725, 7, 2, 9, 5, 8.
My solution was
(50 + 4) x 6 x 3
Solution to 357:
25 x (9 + 5) + 7
Next puzzle:
86975, 3, 7, 10, 1, 4
869! That's a good puzzle. The best so far because other promising methods would come up close.
(3*4+75)=87; 87*10-1=869
Next puzzle:
22425, 75, 4, 6, 8, 7.
My solution was
(10 + 1) x (75 + 4)
Solution to 224:
25 x 6 + 75 + 7 - 8
Next puzzle:
605100, 75, 2, 4, 3, 7
Done it! Here's one solution.
75*7+100-((2+3)*4)
Next puzzle: 284
50, 100, 3, 1, 3, 5
My solution was
(3 x 100) + (4 x 75) + 7 - 2
Solution to 284:
3 x (100 - 5) - 1
Next puzzle:
346100, 75, 7, 5, 5, 2
Solution is here.
75*5-(100/5+7+2)
We''l try 6 small numbers now (Evil isn't it?)
Next puzzle: 650
8, 5, 1, 6, 9, 1.
Not so evil; when the target is an exact multiple of 50 it's easy to see
(9 + 1) x 5 x (8 + 6 - 1)
My solution to 346:
(100 + 75 + 5 - 7) x 2
Next puzzle:
19125, 6, 5, 9, 5, 1
25*6+(9*5-5+1)
Next puzzle: 431
100, 2, 5, 4, 9, 10
Not too difficult:
(100 + 10) x 4 - 9
Next puzzle:
636100, 25, 2, 6, 2, 1
I came up with an interesting solution using all signs and all six numbers.
(100+6)*((25-1)/2/2)
Right then, four large and two small, if you were good at those previous puzzles.
Next puzzle:
999100, 75, 50, 25, 10, 10.
50 x (10 + 10) - (75 + 25) / 100
Next puzzle:
341100, 75, 10, 3, 1, 9
Well done on the 999! I found a solution to 341:
(100+75)*(3-1)-9
Next puzzle: 307
50, 9, 9, 10, 7, 8.
Huh? I'm confused... do we need to use ALL the numbers or just some of them?
No, you don't have to use all the numbers.
This one is really hard! The closest I've got so far is
(9 + 9) x (10 + 7) + 8/50 = 306.16
EDIT:
FINALLY!!!(9 x 7 x 50 / 10) - 8
Next puzzle:
54350, 25, 9, 2, 7, 2
Huh? I'm confused... do we need to use ALL the numbers or just some of them?
You don't need to use all the numbers, although some solutions are necessary to use all.
Whoops I didn't realise Proxima already said that. Anyway, return to the game, a nice looking solution here:
50*9+(25*2*2)-7
Next puzzle: 773
25, 100, 2, 3, 9, 7
(100 x 7) + (25 x 3) - 2
Next puzzle:
96375, 1, 5, 2, 1, 3
960 is all I can do so far.
Are you sure the level is possible?I have finally found it. At least there wasn't a division bit of it.
Here's 963:
(75-1)*(5+2+3)+1
Next puzzle:
537100, 2, 4, 5, 7, 3
It's possible, and you shouldn't set the next puzzle until this one's been solved.
However, this is the solution to 537:
(100 + 2 + 4) x 5 + 7
No next puzzle as the 963 puzzle is still open.
No next puzzle as the 963 puzzle is still open.
OK, I've done it. Bear in mind that some target numbers are impossible. Luckily, none of what we got have happened to be impossible so far.
Now, give me another puzzle!
I have finally found it. At least there wasn't a division bit of it.
Here's 963:
(75-1)*(5+2+3)+1
That sum falls short. It only comes to 741.
In high school I played this game a lot with my friend Daniel, and we wrote down some of the more memorable puzzles that came up. All the ones I'm posting are from that collection, so I know they're all possible

Next puzzle:
351100, 75, 5, 8, 2, 9
(Pooty: I'm sure that's just a typo, should read 5 x 2 + 3, comes to (74 x 13) + 1 which is indeed 963.)
Sorry, it was a typo!

Here we are then. 351 solved. Most numbers used, although not too hard.

(100+75)*2+9-8
Next puzzle:
53675, 9, 10, 2, 4, 7
Ah yes, that is rather simpler than my solution, which was
(100 - 75 + 2) x (8 + 5)
As for 536:
(75 x 7) + 9 + 2
Next puzzle:
232100, 7, 6, 5, 3, 8
232 at last! Here it is...
(7*5-6)*8
Next puzzle:
1498, 5, 9, 2, 6, 6.
There are impossible target numbers? I don't think so, as long as you make sure the numbers you PROVIDE work.
This one is not impossible, but it's hard to find. Here's a solution:
(6+5)*6*2+9+8=149
I really didn't want to do that, but with every puzzle I make, I always check the solver to see if it works.
I've been quietly watching this thread (much as I don't care for post counts, I don't care for forum games either. I do like maths though...), and I thought this was one of the easier ones so far. I found a different solution:
(9 - 6) * 6 * 8 + 5 = 149
My solution was different from either of yours, and used fewer numbers

(9 x 8 x 2) + 5
It bears some resemblance to minimac's solution to my 232 puzzle, which was much more efficient than either Daniel's or mine. Here's how I solved it:
(100 - 8 - 7 - 6) x 3 - 5
Clam Spammer gets to go next

By the way, as regards Dullstar's question, he was right; there are no impossible target numbers. Any target can be made if your numbers include the three digits of the target and two 10s
Clam Spammer gets to go next 
Whoa, hang on a second.
1) I don't have a puzzle to post, and it's getting late here so I won't have one for a while
2) minimac posted a solution so it's already been given away
3) I don't care for forum games, as I just said.
So if you want to post a puzzle now, go ahead.
Okay

Next puzzle:
674100, 50, 10, 7, 3, 3
Not as bad as you think, here's a solution:
(100-10)*7+50-3-3
Next puzzle:
71525, 8, 3, 10, 9, 1
(25 x 10 - 9) - 8
Next puzzle:
478100, 50, 9, 2, 4, 4
I can do 477 so far...
EDIT: I did it!
(50+4)*9-(4*2)
Next puzzle:
846 "The first number shown in the game!"
50, 3, 6, 3, 8, 10
Neat solution, and very different from mine:
(4 x 100) + 50 + ((9 - 2) x 4)
Soluiton to 846 (not too difficult):
(50 - 3) x (8 + 10)
Next puzzle:
348100, 2, 6, 4, 1, 2
Here's 348
(2+1)*100+(2*4*6)
Next puzzle:
90175, 3, 9, 5, 8, 6
Or, since addition is commutative, I can just write (8 + 10) instead of the other way round

901 was far too easy:
75 x (9 + 3) + 6 - 5
Next puzzle:
673100, 4, 9, 10, 3, 6
(This is the 4000th post on the lemmings forums!)
675 is what I can do so far...
EDIT: Finally did it!
(100+10)*6+4+9
Next puzzle:
427
25, 2, 6, 4, 7, 8
Nice one! My solution was more complicated:
(100 + 4 x 3) x 6 + 10 - 9
Solution to 427 (a bit too easy):
25 x (6 + 4 + 7) + 2
Next puzzle:
58450, 25, 9, 5, 9, 8
8*(50+9+5+9)
Next puzzle: 356
75, 6, 10, 7, 3, 7
Excellent puzzle!
6 x (75 - 7 - 7) - 10
I'm all out of puzzles now, I'm afraid...
I Have one
Target number:399
100,3,7,2,90
Although there are only 5 numbers in that puzzle and not 6, it's not too hard.
3*100+90+7+2
Next target: 604
25, 2, 9, 8, 8, 9
Apologies for such a difficult challenge (Or maybe it was just forum game inactivity, I hope this one picks up). The usual rules require you to solve it in 30 seconds.

Anyway here's the solution if you would like to have a look at it.
(25+9)*9*2-8
I've thought of a slightly easier one.
Next target:
499Numbers: 50, 100, 3, 4, 6, 8
I used to play this ALL the time, haha. 2L is my jam ah hahahah
50*8+100-(4-3)
50 75 8 7 4 1 -> 613
Harrrrrrrrd.
50 x 75 / (7-1) = 625. 625 - 8 - 4 = 613.
2 3 4 6 8 =
25 ... for warming up
2 3 4 6 8 25 =
768 ... for the real meat
-- Simon
Not as hard as the last one (I think)
3*8-4+(6/2) = 25
(25-4-3-2)*6*8 = 768
"OK, can I have six small numbers please Rachel"
Next Target:
22310, 6, 5, 9, 5, 4
5*9*5+4-6 = 223 (no need for "10")
I pass my turn for setting the next mystery-number...
This is totally unrelated but I thought I'll post this link to a prank they played on Richard Whitely on countdown back in the day.
This is a must watch as I found it quite funny.
Everyone was in on the prank apart from Richard Whitely who got pranked big time.
http://www.youtube.com/watch?v=TGvhSTno2WM (Remember this is part 1 of 5, the other parts will be there too)