NationStates Jolt Archive

Yay, a new riddles/puzzles/brain teasers/etc thread!

A security guard is locked out of the security office, and he can't remember the 5 digit code required to unlock the door. For simplicity sake lets say the code is abcde.
What the guard does remember(cos he's a wierdo)is:
e+c=14
d+1=b
b+c=10
a+b+c+d+e=30

What are a, b, c, d, and e?

It seems to be a=9, b=4, c=6, d=3, e=8, so the code is 94638.
Show your work.

And feel free to post your own riddles/puzzles/brain teasers/etc

I've got an answer that works, but I'm not convinced about my working.

But I'm fairly sure there's more than one answer, because 'a' can be whatever the hell is left over after you've worked out what b, c, d and e are.

For example, if e=9, then b=5, d=4, c=5, so a must be 7. However, if e=10, b=6, d=5, c=4, so a must be 5, and all the equations still work.

Edit: 10000 posts! Yay!

I've got an answer that works, but I'm not convinced about my working.

But I'm fairly sure there's more than one answer, because 'a' can be whatever the hell is left over after you've worked out what b, c, d and e are.

For example, if e=9, then b=5, d=4, c=5, so a must be 7. However, if e=10, b=6, d=5, c=4, so a must be 5, and all the equations still work.

Edit: 10000 posts! Yay!

There'd only be more than one answer if you can get different numbers for b, c, d and e(as in more than one for b, more than one for c, etc).

And I know it's an example, but e can't be 10.

There'd only be more than one answer if you can get different numbers for b, c, d and e(as in more than one for b, more than one for c, etc).

And I know it's an example, but e can't be 10.
In that case, it's either what I suggested first or the following:

a=9, b=4, c=6, d=3, e=8

I suspect there are multiple solutions. One such solution, by sheer inspection, is

(Despoilered)a = 9
b = 4
c = 6
d = 3
e = 8

However,

a = 11
b = 3
c = 7
d = 2
e = 7

is also a valid solution to the equation (albeit requiring a hex keypad)

Give me a second or two and I'll work out why.

However,

a = 11
b = 3
c = 7
d = 2
e = 7

is also a valid solution to the equation (albeit requiring a hex keypad)
It's a valid solution to the equation but not the riddle, because the code is only five digits.

I suspect there are multiple solutions. One such solution, by sheer inspection, is

a = 9
b = 4
c = 6
d = 3
e = 8

However,

a = 11
b = 3
c = 7
d = 2
e = 7

is also a valid solution to the equation (albeit requiring a hex keypad)

Give me a second or two and I'll work out why.

All the letters represent single digits in a 5 digit code, so the second one is out.

In that case, it's either what I suggested first or the following:

a=9, b=4, c=6, d=3, e=8

It certainly seems to fit.


Bastard, how did you get that so fast?

*feels stupid*

It certainly seems to fit.


Bastard, how did you get that so fast?

*feels stupid*
Because I rock.

Okay here's one.

You are in a room. Three doors including the one you just entered, which is now sealed. There are two brothers, each one with his own door. One has an "A" on his chest, the other has a "B" on his chest. They tell you:

"One door leads to death. One door leads to life."

Which door do you choose? Brother A's or Brother B's?

You can ask them questions if you like.

If you want to know how to do it properly, here's a hint: Solve for A first. :)

In fact, I'll do the first step for you:

a+b+c+d+e=30
b+c=10

therefore. a+10+d+e=30

or

a+d+e=20. :)

Okay here's one.

You are in a room. Three doors including the one you just entered, which is now sealed. There are two brothers, each one with his own door. One has an "A" on his chest, the other has a "B" on his chest. They tell you:

"One door leads to death. One door leads to life."

Which door do you choose? Brother A's or Brother B's?

You can ask them questions if you like.

Isn't there supposed to be more to this? Like one of them always lying and the other always telling the truth?

Isn't there supposed to be more to this? Like one of them always lying and the other always telling the truth?

I won't say anything. Ask them questions if you like. Direct them to Brother A or Brother B or Both respectively.

What the guard does remember(cos he's a wierdo)is:
e+c=14
d+1=b
b+c=10
a+b+c+d+e=30
Okay, I think I've got it. You can eliminate any two variables in the 3 two-term expressions to form a single expression in the remaining two declared variables. However, you only thus have two expressions in 3 unknowns.

Let's work through, eliminating b and d from the 5-term sum.

d = b-1, so
a+2b+c+e = 31

b = 10 - c, so
a-c+e = 11

Given that e = 14 - c, we have
a+3 = 2c

So thus we have that a and c can fulfil the criteria as long as a+3 = 2c.

For instance, if c=0 and a = -3 then b=10, e = 14 and d = 9, which satisfies all the criteria.

Alternatively, you could re-express a in terms of any other variable to determine a similar set of relationships.

It's a valid solution to the equation but not the riddle, because the code is only five digits.
You said nothing about the keypad being decimal. =p

Can we ask both brothers in turn which door leads to life?

Brother A: My Door leads to Life.
Brother B: My Door leads to Life.

Okay here's one.

You are in a room. Three doors including the one you just entered, which is now sealed. There are two brothers, each one with his own door. One has an "A" on his chest, the other has a "B" on his chest. They tell you:

"One door leads to death. One door leads to life."

Which door do you choose? Brother A's or Brother B's?

You can ask them questions if you like.
Can we ask both brothers in turn which door leads to life?

I'm gonna ask Brother A what his brother's name is, then put the same question to Brother B.

(to both) Which door is your door?

*Both Brothers look at you wierd*

Brother's A and B: The Door I'm standing in front of.

We both have our own door's.

Brother A: My Door leads to Life.
Brother B: My Door leads to Life.
(to both) Which door is your door?

P.S There's a little twist in my puzzle that's different from similiar puzzles.

I'm gonna ask Brother A what his brother's name is, then put the same question to Brother B.

P.S There's a little twist in my puzzle that's different from similiar puzzles.

*clears throat loudly*

I'm gonna ask Brother A what his brother's name is, then put the same question to Brother B.


Brother A: He is B.
Brother B: He is B.

*Both Brothers look at you wierd*

Brother's A and B: The Door I'm standing in front of.
Okay. If one brother told the truth just now and the other lied then there is one door that belongs to both of them and one that belongs to neither. In the previous question, it was asserted by both brothers that their door was the door to life. So, we have created a logical inconsistency in the scenario that one must lie and the other must tell truth (even if the liar or truth teller switch roles on a regular or irregular basis).

Both cannot be always telling the truth, for if they are then the doors behind them are both the doors to life and that would render their initial statement (that one is life and the other is death) false.

So let's suppose they're both always lying; that both doors lead to death or to life or neither do. Now, in that case, they're both lying that their own door leads to life, which is the one they're not standing in front of. Therefore, both doors must lead either to death or somewhere else. This the only logically consistent supposition of the liars' game. But, then again, we don't yet know that this is the liars' game.

What else can there be? Perhaps one mimics precisely what the other says; in which case I'd like to hear their response to Ifreann's question next.

EDIT: Ack, you've gone and changed the response! That throws my logic off a bit. Let me think it over.

Rethinking, I think I've still managed to ascertain that the conventional liars' game scenario is not in play, since the inconsistency in that shared statement being both true and false would throw the game to pieces.

Okay. If one brother told the truth just now and the other lied then there is one door that belongs to both of them and one that belongs to neither. In the previous question, it was asserted by both brothers that their door was the door to life. So, we have created a logical inconsistency in the scenario that one must lie and the other must tell truth (even if the liar or truth teller switch roles on a regular or irregular basis).

Both cannot be always telling the truth, for if they are then the doors behind them are both the doors to life and that would render their initial statement (that one is life and the other is death) false.

So let's suppose they're both always lying; that both doors lead to death or to life or neither do. Now, in that case, they're both lying that their own door leads to life, which is the one they're not standing in front of. Therefore, both doors must lead either to death or somewhere else. This the only logically consistent supposition of the liars game. But, then again, we don't yet know that this is the liar's game.

What else can there be? Perhaps one mimics precisely what the other says; in which case I'd like to hear their response to Ifreann's question next.


My Bad. Your question was in fact valid.

Brother A: This is my Door. *Points behind himself*
Brother B: This is my Door. *Points to same door*

EDIT: Bah I had something quite clever in mind, but it fizzled out. Oh well.

Brother A: He is B.
Brother B: He is B.

I see. Brother B appears to immitate Brother A.

Can I ask them the same question, but Brother B first, then Brother A?

I see. Brother B appears to immitate Brother A.

Can I ask them the same question, but Brother B first, then Brother A?

Brother B: He is A.
Brother A: He is B.

Okay here's one.

You are in a room. Three doors including the one you just entered, which is now sealed. There are two brothers, each one with his own door. One has an "A" on his chest, the other has a "B" on his chest. They tell you:

"One door leads to death. One door leads to life."

Which door do you choose? Brother A's or Brother B's?

You can ask them questions if you like.

I ask both brothers "Do you ever lie?"
Then I ask both of them "Does your brother ever lie?"

"If I asked your brother which door leads to 'Life', what would be his answer?"

Brother B: He is A.
Brother A: He is B.

Figured as much. B copies what A says, but A doesn't copy what B says, and they're both telling the truth. Since A has already said that his door leads to life, and we know he's telling the truth, so we go through his door to sweet glorious life.

Unless I'm wrong.

Assuming that each of them will either tell the truth or lie constantly I'd ask any of them: "If I asked whether the door behind you leads to life, what would your answer be ?"
If the answer is "Yes", I'd take that door.
If the answer was "No" I'd take the other door.

Yay, a new riddles/puzzles/brain teasers/etc thread!

A security guard is locked out of the security office, and he can't remember the 5 digit code required to unlock the door. For simplicity sake lets say the code is abcde.
What the guard does remember(cos he's a wierdo)is:
e+c=14
d+1=b
b+c=10
a+b+c+d+e=30

What are a, b, c, d, and e?

It seems to be a=9, b=4, c=6, d=3, e=8, so the code is 94638.
Show your work.

And feel free to post your own riddles/puzzles/brain teasers/etc

e+c=14
d+1=b
b+c=10
a+b+c+d+e=30 e - b = 4

e+c-(b+c)= 14 - 10 = 4
e-b = 4

b+c - (e+c) = 10 - 14 = -4
b-e= -4

b+c +(b-c) = 10 -4
2b = 6
b = 3
3+c = 10, c = 7
3 - e = -4, e= 7
d+1=3
d=2
a+3+7+2+7 = 30

a = 1

hmm I seem to be disagreeing with the spoiler.

b+c - (e+c) = 10 - 14 = -4
b-e= -4

b+c +(b-c) = 10 -4

There's your problem. In the first bit you say that (b+c)=10, which is correct.
You also state that (b-e)= -4, which is also correct.

But then in the second part you state that (b+c) + (b-c) = 10 - 4. (b+c) = 10, but it's (b-e) that equals -4, not (b-c).

a+3+7+2+7 = 30

a = 1
You might want to check that again.

hmm I seem to be disagreeing with the spoiler.
There are only five digits. If a=11, as your working would suggest, that would give six digits. So there's more than one answer to solve the equations, but only one answer that solves the puzzle.

You might want to check that again.


There are only five digits. If a=11, as your working would suggest, that would give six digits. So there's more than one answer to solve the equations, but only one answer that solves the puzzle.
There's more than one valid solution. Try a=7, c=5. So b=5, d=4 and e=9; you'll see that works.

Thus, we have at least 2 different combinations

75549
and
94638

Why the hell is the door I just came through locked? I'd smash it down and get out fast.

I don't see why you should assume that one of them always tells the truth, and one of them always lies. I think I would assume they were normal human beings. However, in this situation, since we know brother B has lied, we should just trust brother A's word.

I got a solution to the security guard problem, but there are clearly several others:

a=7, b=5, c=5, d=4, e=9.

Why the hell is the door I just came through locked? I'd smash it down and get out fast.


Really? I'd headbutt Brother A and shove him through the door. Since the rules which govern the brothers' behaviour could be incredibly complex, I reckon that's the only way to acquire data you can be sure of.

Figured as much. B copies what A says, but A doesn't copy what B says, and they're both telling the truth. Since A has already said that his door leads to life, and we know he's telling the truth, so we go through his door to sweet glorious life.

Unless I'm wrong.

You are correct sir! Enjoy the Paradise that is beyond door A!

Really? I'd headbutt Brother A and shove him through the door. Since the rules which govern the brothers' behaviour could be incredibly complex, I reckon that's the only way to acquire data you can be sure of.

Brother A falls into a Garden of Eden, and the door locks. Brother B in revenge whoops your ass and throws you into door B, where a thousand pains await you.

Brother A falls into a Garden of Eden, and the door locks. Brother B in revenge whoops your ass and throws you into door B, where a thousand pains await you.

I never met a holy man whose ass I couldn't kick!

Okay here's one.

You are in a room. Three doors including the one you just entered, which is now sealed. There are two brothers, each one with his own door. One has an "A" on his chest, the other has a "B" on his chest. They tell you:

"One door leads to death. One door leads to life."

Which door do you choose? Brother A's or Brother B's?

You can ask them questions if you like.http://www.partiallyclips.com/storage/paradox_lg.png

http://www.partiallyclips.com/storage/paradox_lg.png

You win.