My friend is playing a game (don't recall which) and he got stuck on some puzzle or other. The only clue he has is that he must switch on the right lamps to escape.

Well he has 19 lamps in 5 colours, all can either be switched on or off. I've no clue how to even start calculating the combinations. I mean it could be 1 green lamp on with 2 reds. 3 yellows with a blue etc. Seems to me the combinations must run into millions. I told him to go buy something sensible with more logical puzzles as it seems to me he has an impossible task ahead.

Can anyone calculate how many different combinations there are?

The fact that they are in five colours isn't relevant - there are 19 lights and each can be on or off. I think there's a formula for things like that, but I can't remember it off hand. Thats not much help is it...

This isn't one of the Myst series, is it?

Erm... would the game not provide clues?

can each light be turned on to a different color?
ie 19 lights which can be any of 5 different colors (color chosen by the user) on or off?
mmm thats likely to be thousands of possible combinations
or if u cant change the colors and simply have a choice of on or off, then its much lesss combos but still would be a better idea to figure out the riddle of the puzzle rather than trying out each combo. I assume it gave you clues someplace to help out?

The fact that there are 5 colours is highly relevant. The colours are fixed as I understand it. IE 4 blues, 4 reds, 4 greens, 4 yellows and 3 whites. He can't get out until he has the right (combination) of lamps on. His only clue is "don't try to escape until you have the correct lamps on", no more clues than that and no way back out until the lamps are on. I think the combinations must run into millions not thousands. It may be a Myst type game, not sure there. Whatever it is I sure as hell don't want to play it. [img]smile.gif[/img]

NO!!! I should know how to do this stuff in 2 weeks for an exam test :(

- can all lights have 5 colors, which means there's 6 options, one of the colors or off (off would mean no color).
- any hints on the numbers of lamps?

edit: see you already posted it.

[ 11-27-2003, 10:49 AM: Message edited by: philip ]

is the color of the lamps that should be right (like 2 blue and 1 red if there need to be 3 lights on) or is it the lamp itself (like nr.3 nr.6 and nr.9)

If the lights are a fixed colour then the colours are irrelevant. You have 19 lights that can be turned on or off, that will give you the number of combinations available in total. E.g. light one on, lights 2-19 off. If you then try each of those combinations then you'll get the right one eventually regardless of the colour. It'll just take ages.

If you were able to chose the colour the light came on as, therefore providing you with 6 options per light, then the colour would be relevant (and there would be a lot more options...).

[ 11-27-2003, 12:05 PM: Message edited by: Barry the Sprout ]

If a single light only has two possibilities: switched on, or switched off then the total number of possibilities is: 2^19.
If a light can be either switched off or be one of the five colours, then the total number of possibilities is: 5^19.