Solving Brain Teaser #82: Discover Favorite Game, Cost & Hours Played

[tribdog]

When I first bought my XBox I got 5 games to go along with it. I couldn't believe how little money I had left in my pocket when I left the store. I had walked in with nearly $400.00. Nearly half of the total cost was for the games and one of those came with the XBox.
"Splinter Cell" cost as much less than "Prince of Persia" as "Prince of Persia" was less than "Ninja Gaiden."
"Mission Impossible" and "Halo" were the same price, but not the highest.
I played one game for as many hours as the other four combined. That game only cost $0.50 per hour of play, compared to $2.00 per hour for "Mission Impossible"
I've played "Splinter Cell" for the least amount of hours, half as many as the next least played game.
If I awarded medals based on hours played the bronze medal would go to the one I played as long as the non-medal winners combined.
I played my favorite game, which wasn't Halo, for as many hours as another game cost, but not the most expensive one.
Sometimes I'll spend a long time on a difficult stage in a game, that doesn't make it my favorite.

Which game was my favorite, how much did it cost and how many hours did I play it?

 

[Chen]

Woha. I'll get back to you on that.

 

[Chen]

"I played my favorite game for as many hours as another game cost." I don't understand that part?

 

[tribdog]

"I played my favorite game for as many hours as another game cost." I don't understand that part?

example:
I may have played one game for 1000 hours, one game may have cost 1000 dollars. It was played as many hours as the other game cost in dollars

 

[Chen]

Like apples to oranges, but ok. One moment please. Argh I'm lost.

 

[NateTG]

Prince of Persia, $6, 12 Hours

Of course that might not be the only solution,

 

[tribdog]

Prince of Persia, $6, 12 Hours

Of course that might not be the only solution,

Nope. I've never made a problem like this before, so I wasn't sure if I put enough information in or too much but I can show that this answer is incorrect. I'm just not sure how to prove that without giving away the answer.

 

[NateTG]

Nope. I've never made a problem like this before, so I wasn't sure if I put enough information in or too much but I can show that this answer is incorrect. I'm just not sure how to prove that without giving away the answer.

You're right, I misread the problem.

Prince of Persia, 6x hours, $3x

Time played:
1x Splinter Cell
2x Mission Impossible
3x Halo
6x Prince of Persia
12x Ninja Gaiden

Price Paid:
0 Splinter Cell
3x Prince of Persia
4x Mission Impossible
4x Halo
6x Ninja Gaiden

where
0<x<\frac{200}{17}

 

[Njorl]

Who cares about you silly games, what's the brain teaser!?

...oh...

 

[jamesrc]

You're right, I misread the problem.

Prince of Persia, 6x hours, $3x

Time played:
1x Splinter Cell
2x Mission Impossible
3x Halo
6x Prince of Persia
12x Ninja Gaiden

Price Paid:
0 Splinter Cell
3x Prince of Persia
4x Mission Impossible
4x Halo
6x Ninja Gaiden

where
0<x<\frac{200}{17}

I agree, but isn't "Halo" as the favorite game also a valid solution? (Hours played = 3x (which is the same as the cost of "Prince of Persia"), Cost = 4x.)

And do you remember how you decided which game was played for 3x hours and which was played for 6x hours? The reason I ask is I'm missing that part, which would allow hours for "Prince of Persia" to = 3x and hours for "Halo" to equal 6x. This would give an additional solution of favorite game = Halo, Time = 6x hours, and cost = 4x dollars. (Prince of Persia would then have time=3x hours and cost = 3x dollars, which would not be a valid solution as the "favorite game".)

 

[tribdog]

I looked at all of my money and I couldn't find an X on any of them, so I'm going to say No right answers so far , No that's not true. lol. my fault I thought I had eliminated the possibility of more than one correct answer. This is my first attempt at a problem. Can I add something? sure I can it's my brain teaser. Dollars must be whole numbers, no cents and here's my new limiter I want to change this line:
I played my favorite game, which wasn't Halo, for as many hours as another game cost, but not the most expensive one.

 

[PRodQuanta]

Ok, a little confusing. I still may be off, but here is my answer. I'm going to put 4 down out here.

Prince of Persia
$92
69 hours

POP
$69
138 hours

POP
$69
69 hours

MI
$92
46 hours

I'm either a)on, or b)I'm so off, I'm almost on. Sorry if I'm b.

Paden Roder