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

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Discussion Overview

The discussion revolves around a brain teaser involving the costs and hours played for various video games associated with an Xbox. Participants are attempting to deduce the favorite game, its cost, and the hours played based on a set of clues provided in the initial post. The scope includes problem-solving, logical reasoning, and mathematical relationships among the games.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant notes that the favorite game was played for as many hours as another game cost, leading to confusion about the interpretation of this statement.
  • Another participant suggests that "Prince of Persia" could cost $6 and be played for 12 hours, but acknowledges this may not be the only solution.
  • There are claims that "Halo" could also be a valid favorite game, depending on the hours played and costs assigned to other games.
  • A participant expresses uncertainty about how to prove their answer is incorrect without revealing the solution.
  • One participant introduces a new constraint that all dollar amounts must be whole numbers, clarifying the conditions of the problem.
  • Another participant presents a potential solution involving various games and their respective costs and hours played, but expresses uncertainty about its correctness.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the favorite game, its cost, or the hours played. Multiple competing views and interpretations of the clues remain, with some participants suggesting different potential solutions.

Contextual Notes

Participants note the complexity of the problem and the potential for multiple interpretations. There is an emphasis on the need for whole number costs and the implications of the clues provided, which may lead to different conclusions.

Who May Find This Useful

This discussion may be of interest to those who enjoy logic puzzles, mathematical reasoning, or problem-solving related to game mechanics and costs.

tribdog
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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?
 
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Woha. I'll get back to you on that. :wink:
 
"I played my favorite game for as many hours as another game cost." I don't understand that part?
 
Chen said:
"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
 
Like apples to oranges, but ok. :smile: One moment please. Argh I'm lost. :mad:
 
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Prince of Persia, $6, 12 Hours

Of course that might not be the only solution,
 
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NateTG said:
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.
 
tribdog said:
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}
 
Who cares about you silly games, what's the brain teaser!?

...oh...
 
  • #10
NateTG said:
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".)
 
  • #11
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.
 
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  • #12
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
 

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