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Topic: Light Bulbs And Switches Variation 2 (Read 17100 times) |
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alien2
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Light Bulbs And Switches Variation 2
« on: Oct 13th, 2020, 3:10am » |
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You are in a room with sixteen* light switches, each of which controls one of sixteen (incandescent) light bulbs in the next room. Your task is to determine which switch controls which bulb. All lights are initially off, and you can't see into one room from the other. You are allowed only two chances to enter the room with the light bulbs. You must close the door each time you enter or leave the room with the light bulbs. How can you determine which light switch goes with which light bulb?
* I modified the riddle. Instead of 11 there's 16 light bulbs.
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| « Last Edit: Oct 26th, 2020, 6:22am by alien2 » |
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rmsgrey
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Re: Light Bulbs And Switches Variation 2
« Reply #1 on: Oct 13th, 2020, 3:01pm » |
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If I can distinguish 4 with one visit, I can distinguish 16 with two visits (and sufficient time).
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alien2
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Re: Light Bulbs And Switches Variation 2
« Reply #2 on: Oct 13th, 2020, 3:25pm » |
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Check out the big brain on rmsgrey! I am still stuck at 11 bulbs.
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rmsgrey
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Re: Light Bulbs And Switches Variation 2
« Reply #3 on: Oct 14th, 2020, 11:15am » |
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on Oct 13th, 2020, 3:25pm, alien2 wrote:| Check out the big brain on rmsgrey! I am still stuck at 11 bulbs. |
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In general, if you can distinguish between n cases in one test, two tests will let you distinguish between n2.
For example, in a scenario with 4 cases, call them A, B, C and D, there are 16 possible outcomes from the two tests:
AA, AB, AC, AD
BA, BB, BC, BD
CA, CB, CC, CD
DA, DB, DC, DD
For a simpler example with light-bulbs, if you can only distinguish 2 cases - on and off - then in two visits you can identify up to 4 bulbs with their switches: label the switches 0, 1, 2 and 3. Before your first visit, turn off 0 and 1, and on 2 and 3. Before your second visit, turn off 0 and 2, and on 1 and 3. On your visits, for each bulb, jot down a 1 if it's lit; a 0 if it's not (putting later labels for each bulb directly to the right of earlier labels). After the two visits, you'll have written down a binary number for each bulb, corresponding to the switch that controls it.
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alien2
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Re: Light Bulbs And Switches Variation 2
« Reply #4 on: Oct 14th, 2020, 11:28am » |
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You're right. One can discern 16 light bulbs. There are four groups with each group consisting of four light bulbs you discern on your 1st visit.
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| « Last Edit: Oct 15th, 2020, 3:32am by alien2 » |
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Grimbal
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Re: Light Bulbs And Switches Variation 2
« Reply #5 on: Oct 25th, 2020, 12:51pm » |
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You need only one visit.
Turn all switches off. Turn the first switch on, wait a month, turn the second switch on, wait a month, etc. until the last. Then go to the room and observe in which order the bulbs burn out over the next few months.
That's all!
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alien2
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Re: Light Bulbs And Switches Variation 2
« Reply #6 on: Oct 26th, 2020, 5:00am » |
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Sure. And if you're Superman all you need is a couple of seconds since you've X-Ray vision and you can see through the walls. -_-
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rmsgrey
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Re: Light Bulbs And Switches Variation 2
« Reply #7 on: Oct 26th, 2020, 11:22am » |
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on Oct 25th, 2020, 12:51pm, Grimbal wrote:You need only one visit.
Turn all switches off. Turn the first switch on, wait a month, turn the second switch on, wait a month, etc. until the last. Then go to the room and observe in which order the bulbs burn out over the next few months.
That's all! |
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Google tells me that the typical lifespan of an incandescent bulb is 1000 hours - or 6 weeks. So, after 15 months of turning on one switch per month, you'd expect 14 bulbs to already be burnt out by the time you go through - maybe only 13.
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rmsgrey
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Re: Light Bulbs And Switches Variation 2
« Reply #9 on: Oct 28th, 2020, 12:13pm » |
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on Oct 28th, 2020, 11:27am, towr wrote:
That light pre-dates the Phoebus Cartel - which, among other things, set the standard lifespan of an incandescent bulb to 1000 hours, fining manufacturers who produced bulbs that lasted longer.
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towr
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Re: Light Bulbs And Switches Variation 2
« Reply #10 on: Oct 29th, 2020, 11:57am » |
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That cartel ceased operations in the second world war. And I see no mention they enforced a minimum life expectancy. I also very much doubt they fined based on maximum life of a light bulb.
page 5 on of this document has an example distribution based on empirical data.
It's close enough to a normal distribution for arguments sake, with a pretty significant standard deviation. (Although there are better fitting distributions, like log-normal.)
So basically, time-to-failure will not be a reliable method to find out which bulb is controlled by which switch.
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| « Last Edit: Oct 29th, 2020, 12:03pm by towr » |
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Wikipedia, Google, Mathworld, Integer sequence DB
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