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## Question

If you are in a room with 5 coloured light switches(White,Red,Blue,Yellow,and Green),and you don`t know which one is on(ON) position and which is on(OFF) position.

You`ve been told to screw 5 coloured light bulbs(white,red,blue,yellow,and green)down in the basement,where there are 5 places ,one place for each bulb.

Your goal is to connect each bulb to its corresponding switch,with minimal times going down to the basement.

Note:

You have to use these bulbs only ,i.e. No instruments.

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3 goes, I don't think lower is possible.

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I agree with James22, post #2.

Switches installed right side up, as any electrician would do, are off in the down position and on in the up position so we know from position if on or off. Turn on W, R & B keep Y & G off. Make first trip to basement use bulbs to determine which are lit and screw W, R & B into the ones on and Y & G into ones off. Return to switches and turn on Y and turn off W. Trip 2 to basement If Y is lit then Y & G are correct. If G lit switch it with Y leaving Y & G in correct position. Bulb that is off of the other three should be white, if not switch with that one with white. At this point W, Y & Green are correct, Return to switches and turn off R, Basement trip 3 if R is off, everything is correct, if R is on, then swap it with B leaving all correct. Of course don't forget to wear insulated gloves for changing hot bulbs.

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Clarification: When you say that we don't know which position is on and which position is off, do you mean

1) There are two possibilities which are [all of the switches are "on" in the "up" position and "off" in the "down" position] or [all of the switches are "off" in the "up" position and "on" in the "down" position]

or

2) Any switch can be "on" in the "up" position and "off" in the "down" position or vice-versa, regardless of which positions are "on" and "off" for each of the other switches

If you mean #1, then I agree with the answers above. If you mean #2, it gets more complicated.

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Clarification: When you say that we don't know which position is on and which position is off, do you mean

1) There are two possibilities which are [all of the switches are "on" in the "up" position and "off" in the "down" position] or [all of the switches are "off" in the "up" position and "on" in the "down" position]

or

2) Any switch can be "on" in the "up" position and "off" in the "down" position or vice-versa, regardless of which positions are "on" and "off" for each of the other switches

If you mean #1, then I agree with the answers above. If you mean #2, it gets more complicated.

I did overlook the part of the problem that said we could not determine "OFF" or "ON" position. If we can assume that at least they were wired consistently, then James22 is still correct in my opinion

by switching 3 one way and 2 the other, when we get to the basement we can positively identify which way is in fact "ON" and which way is "OFF" and proceed basically as I described before.

If we are to assume that the electrician bought switches that had no indications of direction and randomly wired the switches, then the problem is more complex and more trips will be required.

4 trips necessary:

Turn all switches in same direction; Trip one go to basement, screw 5 bulbs into 5 sockets and note which are on and which are off. Method is now similar to my explanation in post #3 Return to switches and change positions of 3 switches (W, R & B) and trip two to basement Lights with changed status are W, R & B those unchanged are Y & G. At switches, turn Y & W trip three to basement. Of the Y-G group, the one changed is Y and the other is G and the one with changed status in W, R B group is W. At switches, flip R, and trip four to the basement the changed status must be R leaving by elimination B as the one that never changed. By referring to notes on the original lights status and switch positions , we also know which way is "ON" and can label them.

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It is clear from the puzzle (though one has to read very carefully) that the ON & OFF position of switches is not known. Now we know that all switches must have their ON - OFF position in only one direction. So before making first trip to the basement you put three switches in one direction and other two switches in opposite direction. Then you will find either [1] three bulbs (say W, R, B) ON and two bulbs (say Y, G) OFF, OR [2] Three bulbs OFF (say W, R, B) and two bulbs (say Y, G) ON. So in first trip you are able to know two groups of places for three bulbs (say W, R, B) and two bulbs (say Y, G) respectively. Now you reverse the position of one switch in each group (say of R & G). Then in second trip you know the exact position of three bulbs (R, Y, G).

Now you reverse the position of one of the switches (say W) of two still unknown places. So in third trip you are able to know the right places for rest of the two bulbs (in example W & B).

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It is clear from the puzzle (though one has to read very carefully) that the ON & OFF position of switches is not known. Now we know that all switches must have their ON - OFF position in only one direction. So before making first trip to the basement you put three switches in one direction and other two switches in opposite direction. Then you will find either [1] three bulbs (say W, R, B) ON and two bulbs (say Y, G) OFF, OR [2] Three bulbs OFF (say W, R, B) and two bulbs (say Y, G) ON. So in first trip you are able to know two groups of places for three bulbs (say W, R, B) and two bulbs (say Y, G) respectively. Now you reverse the position of one switch in each group (say of R & G). Then in second trip you know the exact position of three bulbs (R, Y, G).

Now you reverse the position of one of the switches (say W) of two still unknown places. So in third trip you are able to know the right places for rest of the two bulbs (in example W & B).

That reading the OP makes it sound like each switch could have different direction for "on" and "off"...which means you could have all of the switches in the DOWN position, walk downstairs and find 3 bulbs ON, and 2 OFF (or 1 on, 4 off, etc...). In other words, I agree with thoughtfulfellow in his second assumption. I think we need clarification from wolfgang on this one.

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Clarification: When you say that we don't know which position is on and which position is off, do you mean

1) There are two possibilities which are [all of the switches are "on" in the "up" position and "off" in the "down" position] or [all of the switches are "off" in the "up" position and "on" in the "down" position]

or

2) Any switch can be "on" in the "up" position and "off" in the "down" position or vice-versa, regardless of which positions are "on" and "off" for each of the other switches

If you mean #1, then I agree with the answers above. If you mean #2, it gets more complicated.

any switch can be(ON) either when it is (up) or ( down),they may be all(OFF) even if they were in different directions(up or down).

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I agree with thoughtfulfellow..

4 trips!

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any switch can be(ON) either when it is (up) or ( down),they may be all(OFF) even if they were in different directions(up or down).

In that case one more trip i.e. 4 trips will be required to complete the task.

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I want you to do it with only three trips.....

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FIRST TRIP: Put all five bulbs randomly, any bulb in any place. We find following conditions:

[1] All bulbs are OFF.

[2] All bulbs are ON.

[3] One bulb (say X) is ON, four bulbs are OFF.

[4] Two bulbs are ON, Three bulbs are OFF.

[5] Three bulbs are ON, two bulbs are OFF.

[6] Four bulbs are ON, one bulb (say Z) is OFF.

CONDITION [1] & [2]:

It is easy because ON & OFF directions, for all switches become known immediately.

SECOND TRIP: Next step is to keep two switches OFF (say W & G), and three switches (say R, Y, & B) ON for enough time to warm the bulbs. Then put out one bulb (say B), and enter the basement immediately to find one bulb which should be hot and OFF. So this is the place for Blue bulb.

Now find out the two cool OFF bulbs, these are the places for W & G.

Find two bulbs which are ON, these are the places for R & Y bulbs.

THIRD TRIP: Now out of R & Y, keep one bulb (say R) OFF, and one bulb (say Y) ON.. Also out of W & G, keep one bulb (say G) ON, and one bulb (say W) OFF. Now enter the basement and find the ON bulb in the place for R & Y bulbs, and similarly in the place for W & G bulbs.

Thus you know the right places for all the five bulbs in three trips to basement.

CONDITION [3] & [6]:

Reverse the position of any three switches (say of R, Y, & B), then at least two bulbs will become ON, and bulb X might have become OFF; or three other bulbs might have become ON, and X is already ON. Keep the switches in this position for enough time to warm the bulbs and then change the position of one switch (say of R) to original position. Then,

[a] Two Bulbs may be found ON, one may be found warm and OFF, X may be found ON, one bulb is cool and OFF.

Two bulbs and X bulb may be found ON, two bulbs are cool and OFF.

[c] X may be found OFF and cool, one bulb may be found warm and OFF, one bulb may be found ON, two bulbs are cool and OFF.

SECOND TRIP: [a] If we find a bulb which is warm and OFF then that is the place for R bulb. Then if we find bulbs at two more places have become ON, these two places are for Y & B bulbs. And then the place X, and the place where bulb is cool & OFF, are the places for W & G bulbs.

Now if we find no any warm bulb which is OFF, and if X is found ON, then this is the place for R bulb. Then there will be two more places where the bulbs will be found ON, they are the places for Y & B bulbs, and the places where two bulbs are cool and OFF, they are the places for W & G bulbs.

[c] If X is found OFF and cool, and one new place is found where bulb became ON, then these are the places for Y & B, then one place is found where bulb is found warm and OFF, that is the place for bulb R; then the places where two cool and Off bulbs are found, are the places for W & G.

Now by adopting similar procedure as adopted above in Condition [1] & [2], we may find out the correct places for other bulbs also.

Similar procedure may be adopted for all other conditions.

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FIRST TRIP: Put all five bulbs randomly, any bulb in any place. We find following conditions:

[1] All bulbs are OFF.

[2] All bulbs are ON.

[3] One bulb (say X) is ON, four bulbs are OFF.

[4] Two bulbs are ON, Three bulbs are OFF.

[5] Three bulbs are ON, two bulbs are OFF.

[6] Four bulbs are ON, one bulb (say Z) is OFF.

CONDITION [1] & [2]:

It is easy because ON & OFF directions, for all switches become known immediately.

SECOND TRIP: Next step is to keep two switches OFF (say W & G), and three switches (say R, Y, & B) ON for enough time to warm the bulbs. Then put out one bulb (say B), and enter the basement immediately to find one bulb which should be hot and OFF. So this is the place for Blue bulb.

Now find out the two cool OFF bulbs, these are the places for W & G.

Find two bulbs which are ON, these are the places for R & Y bulbs.

THIRD TRIP: Now out of R & Y, keep one bulb (say R) OFF, and one bulb (say Y) ON.. Also out of W & G, keep one bulb (say G) ON, and one bulb (say W) OFF. Now enter the basement and find the ON bulb in the place for R & Y bulbs, and similarly in the place for W & G bulbs.

Thus you know the right places for all the five bulbs in three trips to basement.

CONDITION [3] & [6]:

Reverse the position of any three switches (say of R, Y, & B), then at least two bulbs will become ON, and bulb X might have become OFF; or three other bulbs might have become ON, and X is already ON. Keep the switches in this position for enough time to warm the bulbs and then change the position of one switch (say of R) to original position. Then,

[a] Two Bulbs may be found ON, one may be found warm and OFF, X may be found ON, one bulb is cool and OFF.

Two bulbs and X bulb may be found ON, two bulbs are cool and OFF.

[c] X may be found OFF and cool, one bulb may be found warm and OFF, one bulb may be found ON, two bulbs are cool and OFF.

SECOND TRIP: [a] If we find a bulb which is warm and OFF then that is the place for R bulb. Then if we find bulbs at two more places have become ON, these two places are for Y & B bulbs. And then the place X, and the place where bulb is cool & OFF, are the places for W & G bulbs.

Now if we find no any warm bulb which is OFF, and if X is found ON, then this is the place for R bulb. Then there will be two more places where the bulbs will be found ON, they are the places for Y & B bulbs, and the places where two bulbs are cool and OFF, they are the places for W & G bulbs.

[c] If X is found OFF and cool, and one new place is found where bulb became ON, then these are the places for Y & B, then one place is found where bulb is found warm and OFF, that is the place for bulb R; then the places where two cool and Off bulbs are found, are the places for W & G.

Now by adopting similar procedure as adopted above in Condition [1] & [2], we may find out the correct places for other bulbs also.

Similar procedure may be adopted for all other conditions.

What if the bulbs are LED? Then insufficient residual heat to feel any difference. With the assumption of incandescent bulbs, that is a clever solution.

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FIRST TRIP: Put all five bulbs randomly, any bulb in any place. We find following conditions:

[1] All bulbs are OFF.

[2] All bulbs are ON.

[3] One bulb (say X) is ON, four bulbs are OFF.

[4] Two bulbs are ON, Three bulbs are OFF.

[5] Three bulbs are ON, two bulbs are OFF.

[6] Four bulbs are ON, one bulb (say Z) is OFF.

CONDITION [1] & [2]:

It is easy because ON & OFF directions, for all switches become known immediately.

SECOND TRIP: Next step is to keep two switches OFF (say W & G), and three switches (say R, Y, & B) ON for enough time to warm the bulbs. Then put out one bulb (say B), and enter the basement immediately to find one bulb which should be hot and OFF. So this is the place for Blue bulb.

Now find out the two cool OFF bulbs, these are the places for W & G.

Find two bulbs which are ON, these are the places for R & Y bulbs.

THIRD TRIP: Now out of R & Y, keep one bulb (say R) OFF, and one bulb (say Y) ON.. Also out of W & G, keep one bulb (say G) ON, and one bulb (say W) OFF. Now enter the basement and find the ON bulb in the place for R & Y bulbs, and similarly in the place for W & G bulbs.

Thus you know the right places for all the five bulbs in three trips to basement.

CONDITION [3] & [6]:

Reverse the position of any three switches (say of R, Y, & B), then at least two bulbs will become ON, and bulb X might have become OFF; or three other bulbs might have become ON, and X is already ON. Keep the switches in this position for enough time to warm the bulbs and then change the position of one switch (say of R) to original position. Then,

[a] Two Bulbs may be found ON, one may be found warm and OFF, X may be found ON, one bulb is cool and OFF.

Two bulbs and X bulb may be found ON, two bulbs are cool and OFF.

[c] X may be found OFF and cool, one bulb may be found warm and OFF, one bulb may be found ON, two bulbs are cool and OFF.

SECOND TRIP: [a] If we find a bulb which is warm and OFF then that is the place for R bulb. Then if we find bulbs at two more places have become ON, these two places are for Y & B bulbs. And then the place X, and the place where bulb is cool & OFF, are the places for W & G bulbs.

Now if we find no any warm bulb which is OFF, and if X is found ON, then this is the place for R bulb. Then there will be two more places where the bulbs will be found ON, they are the places for Y & B bulbs, and the places where two bulbs are cool and OFF, they are the places for W & G bulbs.

[c] If X is found OFF and cool, and one new place is found where bulb became ON, then these are the places for Y & B, then one place is found where bulb is found warm and OFF, that is the place for bulb R; then the places where two cool and Off bulbs are found, are the places for W & G.

Now by adopting similar procedure as adopted above in Condition [1] & [2], we may find out the correct places for other bulbs also.

Similar procedure may be adopted for all other conditions.

Very good!!

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I can do it in 3 trips n.b this was done on the assumption that the bulbs will turn on in their incorrect positions

Trip 1:put in all the bulbs in any places(order does not matter now) and note which are on and off.

After Leaving 1: switch the positions of 3 switches and leave the other 2 untouched

Trip 2: Note which bulbs have changed from on to off or vice versa in this case let it be r, b and y (group 1) and the w and g (group)2 are unchanged

After leaving 2: turn all group 1 off (if we identified the groups we also Identified the on/off positions) and leave 1 on (tet it be b) and wait for a while then turn it off then swich another one from group 1(let it be r) on and swich the positions of one of the group 2's (let it be g)

Trip 3:the one thats on from group 1 is r and the one that's on from group 2 is g and by exclusion the other one is w the 2 remaining bulbs feel them both and you will see that b will be warmer than y because b was left on for a while

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