1. More than 2 Lights are OFF

2. Any OFF Light must not have exactly one adjacent ON light.

Given that 1 is False and 2 is TRUE, how many different unique arrangements are possible?

1. 5

2. 9

3. 12

4. 16

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- Thread starter tod
- Start date

1. More than 2 Lights are OFF

2. Any OFF Light must not have exactly one adjacent ON light.

Given that 1 is False and 2 is TRUE, how many different unique arrangements are possible?

1. 5

2. 9

3. 12

4. 16

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Perhaps a good place to start would be to provide your method and how you got the answer 5.My answer was 5

7 on = ooooooo

6 on combos noting no 1s allowed

0-6 = xoooooo

2-4 = ooxoooo

3-3 = oooxooo

5 on combos

0-0-5 = xxooooo

0-2-3 = xooxooo

0-3-2 = xoooxoo

0-5-0 = xooooox

2-0-3 = ooxxooo

This assumes mirror images (eg. 4-2 vs 2-4, 3-0-2 vs 2-0-3) don't count. If included they add up to 15 but is not in the answers.

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I don't necessarily agree that statement one being FALSE means there are 0, 1, or 2 lights on. I'd interpret it as meaning more than two lights are on... how do you come to your conclusion, @A1? What am I interpreting incorrectly?

7 on = ooooooo

6 on combos noting no 1s allowed

0-6 = xoooooo

2-4 = ooxoooo

3-3 = oooxooo

5 on combos

0-0-5 = xxooooo

0-2-3 = xooxooo

0-3-2 = xoooxoo

0-5-0 = xooooox

2-0-3 = ooxxooo

This assumes mirror images (eg. 4-2 vs 2-4, 3-0-2 vs 2-0-3) don't count. If included they add up to 15 but is not in the answers.

All questions are worth more than one point. Just to clarify, do you mean if there weren't multiple questions based on the same stimulus?its 16

because the combinations go upto more than 12 lol.

but i wouldnt waste ime on that question if its just 1 pointer,

yeah, !!! I mean if its just one question based on a big excerpt....All questions are worth more than one point. Just to clarify, do you mean if there weren't multiple questions based on the same stimulus?

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More than 2 lights on can make but does not guarantee the statement false. Like 4 on + 3 off, the latter makes it true.I don't necessarily agree that statement one being FALSE means there are 0, 1, or 2 lights on(??). I'd interpret it as meaning more than two lights are on...

So this is the way I saw it.Perhaps a good place to start would be to provide your method and how you got the answer 5.

From Rule 1, we say that 0,1 or 2 lights are off.

'Any OFF Light must not have exactly one adjacent ON light.'

If we take this as xxxxxxx, we can already exclude the off lights from being on either end of the sequence as this would mean there is only 1 adjacent ON light if the on light was 2nd in the sequence.

So you would be left with five possible places for the off lights.

xxxxxxx

x0xxxxx

x0x0xxx

x0xx0xx

x0xxx0x

xx0x0xx

xx0xx0x

xxx0x0x

xx0xxxx

xxx0xxx

xxxx0xx

xxxxx0x

....actually i just realised its a hec more than five

Guess the answer was 12

Last edited:

Oops my interpretation above of the rule 2 was incorrect. Indeed it means an Off light must be between two On lights, and 12 is the answer.'Any OFF Light must not have exactly one adjacent ON light.'

If we take this as xxxxxxx, we can already exclude the off lights from being on either end of the sequence

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So if you have two statements:

1. More than 2 Lights are OFF - False (essentially, you have the statement that there are 0, 1, or 2 lights off)

2. Any OFF Light must not have exactly one adjacent ON light

for 0 lights off, there is 1 combination (all on)

for 1 light off, there are exactly five combinations (the single off light being anywhere except either end)

for 2 lights off, as per Rule 2, the off lights cannot be on either end and the off lights cannot be adjacent to each other. Basically this means in the middle 5 lights, you have (where 1 is an OFF light)

lights 4 apart x 1 10001

lights 3 apart x 2 10010 and 01001

lights 2 apart x 3 10100 01010 00101

This gives the requisite 12.

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