## Who is What?

A forum for good logic/math puzzles.

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qwng
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### Who is What?

David and Edward are brothers. one is a programmer and the other is an engineer. David is exactly 26 weeks older than Edward who was born in August. The programmer, who was born in January, was 54 years old in 1998. Which of the two is the engineer??

Source: The Magic Garden of George B And Other Logic Puzzles - Raymond Smullyan (World Scientific Publishign)

somehow
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### Re: Who is What?

Am I missing something? This looks... not puzzling.

Spoiler:
Edward was born in August. The programmer was born in January, so Edward is not the programmer, and thus Edward is the engineer.

Is the trick supposed to be the extraneous information (54 years old in 1998, 26 weeks older, etc.)?
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SteelCamel
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### Re: Who is What?

Spoiler:
I agree that most of the information seems to be irrelevant, but when you look closer it seems that solution cannot be correct.

The programmer was born in January. The programmer was 54 in 1998, so was born in January 1944, which is a leap year.
Edward was born in August. David is 26 weeks older, so he was born 26 weeks earlier. However the only date in January that is 26 weeks before one in August is 31 January, which is 26 weeks before 1 August - as long as it's not a leap year. So David cannot be the programmer. Edward also cannot be the programmer as he cannot have been born in both August and January.
Also, two brothers with only 6 months age difference?

Either the puzzle is just wrong, or we're missing some kind of hidden meaning in the wording. I'm inclined to think it's wrong.

somehow
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Joined: Wed Aug 14, 2013 8:31 pm UTC

### Re: Who is What?

Spoiler:
Hmm. Well, it seems worth noting that it's possible to "be 54 years old in 1998" either by being born in 1944 and turning 54 in 1998 or by being born in 1943 and being 54 years old at the start of 1998.
Xenomortis wrote:O(n2) takes on new meaning when trying to find pairs of socks in the morning.

Cauchy
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### Re: Who is What?

I looked up Smullyan's solution, and it's... lacking.

It makes me not want to read his book, honestly.
(∫|p|2)(∫|q|2) ≥ (∫|pq|)2
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phlip
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### Re: Who is What?

Cauchy wrote:I looked up Smullyan's solution, and it's... lacking.

Wow... yeah.

For reference:
Spoiler:
Smullyan wrote:If David is the programmer, we get the following contradiction: David was then born in January (since the programmer was) and is exactly 26 weeks older than Edward, who was born in August. But this is only possible if David was born on January 31 and Edward on August 1 and there is no February 29 in between-in other words, that it is not a leap year. [You can check this with a calendar]. Thus, if David is the programmer, then he was not born on a leap year. On the other hand, if David is the programmer, he was 54 years old in January 1998, hence he was born in 1944, which is a leap year! Thus, it is contradictory to assume that David is the programmer, and so David must be the engineer.

Which completely avoids the point that having Edward be the programmer leads much more directly to a rather simpler contradiction directly from the puzzle statement...

The logic makes about as much sense as:
Q: I have a weight that's either 3kg or 5kg. I put it on a scale balance against a 1kg weight and found it to be lighter. How heavy is the weight?
A: Well, if we assume it's the 3kg weight, then we arrive at a contradiction, because 3kg > 1kg, so therefore it must be 5kg.

Or, to put it another way: the question is contradictory, and you can derive anything from a contradiction.

Code: Select all

`enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}`
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SPACKlick
Posts: 195
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### Re: Who is What?

I disagree that this is contradictory it is trivial

Spoiler:
David is the programmer born on the 31/01/1943 and Edward is the Engineer born on 01/08/1943 to the same mother and father

Breaking down the facts individually

1. David and Edward are brothers [Irrelevant but creepy given the age gap]
2. {{J(David), J(Edward)}} = {{Programmer, Engineer}} [J(x) = role of x]
3. B(David)+182 = B(Edward) [B(x) = birth date of x]
4. M(B(Edward)) = 08 [M(x) = month of date x]
5. M(B(Programmer) = 01
The next one can be interpreted two ways, Literal
6a. 02/01/1943 < B(Programmer) < 31/12/1944
Common parlance

So it is clear that Edward isn't the programmer from 4 and 5 and the fact that individuals can only have one birthday and dates can only have one month.

All that remains is to ask is there a contradiction or not if J(David) = programmer.

If David is the programmer born on the 31/01/1943 and Edward is the Engineer born on 01/08/1943 to the same mother and father. then
1) They are brothers
2) One brother is a programmer and the other is an engineer
3) Edward is born exactly 26 weeks after David making David 26 weeks older
4) Edward was born in August
5) The programmer was born in January
6a) From 01/01/1998 to 30/01/1998 the programmer is 54.

There's nothing interesting here.

Smullyan's answer seems to assume a different version of 6
6b. 01/01/1944 < B(Programmer) < 31/12/1944

Demki
Posts: 199
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### Re: Who is What?

SPACKlick wrote:I disagree that this is contradictory it is trivial

Spoiler:
David is the programmer born on the 31/01/1943 and Edward is the Engineer born on 01/08/1943 to the same mother and father

Breaking down the facts individually

1. David and Edward are brothers [Irrelevant but creepy given the age gap]
2. {{J(David), J(Edward)}} = {{Programmer, Engineer}} [J(x) = role of x]
3. B(David)+182 = B(Edward) [B(x) = birth date of x]
4. M(B(Edward)) = 08 [M(x) = month of date x]
5. M(B(Programmer) = 01
The next one can be interpreted two ways, Literal
6a. 02/01/1943 < B(Programmer) < 31/12/1944
Common parlance

So it is clear that Edward isn't the programmer from 4 and 5 and the fact that individuals can only have one birthday and dates can only have one month.

All that remains is to ask is there a contradiction or not if J(David) = programmer.

If David is the programmer born on the 31/01/1943 and Edward is the Engineer born on 01/08/1943 to the same mother and father. then
1) They are brothers
2) One brother is a programmer and the other is an engineer
3) Edward is born exactly 26 weeks after David making David 26 weeks older
4) Edward was born in August
5) The programmer was born in January
6a) From 01/01/1998 to 30/01/1998 the programmer is 54.

There's nothing interesting here.

Smullyan's answer seems to assume a different version of 6
6b. 01/01/1944 < B(Programmer) < 31/12/1944

The thing about them being brothers is crucial, given that human birth takes 9 months. The only 2 explanations I can think of:
1. They are step-brothers or really close friends.
2. They are twins, and either one of them was removed incredibly early, or the other was incredibly late, or both(probably not possible, is it possible to delay birth by 3 months? Or give birth 3 months early?)

somehow
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Joined: Wed Aug 14, 2013 8:31 pm UTC

### Re: Who is What?

... also adoption is a thing?
Xenomortis wrote:O(n2) takes on new meaning when trying to find pairs of socks in the morning.

SDK
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### Re: Who is What?

I've known families with kids almost that close. According to google: "about 50 percent of babies born at 24 weeks survive", so it is technically possible that they're normal brothers, just that Edward was born very premature.
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jestingrabbit
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### Re: Who is What?

SDK wrote:I've known families with kids almost that close. According to google: "about 50 percent of babies born at 24 weeks survive", so it is technically possible that they're normal brothers, just that Edward was born very premature.

I expect that that's with our very full on antenatal care regimes. Adoption makes heaps more sense.

But overall, this feels pretty deeply flawed as a logic puzzle.
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SDK
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### Re: Who is What?

I guess that's also current stats, not from back in 1944. Okay, adoption it is! Puzzle solved!

(Sorry, forgot to spoiler the answer)
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SPACKlick
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### Re: Who is What?

I suspect the puzzle is trying to be a different puzzle entirely
Spoiler:
where we assume that all references to "The Engineer" and "The Programmer" can refer to any engineer/programmer rather than a specific one and that one of the brothers is both so what appears to be a contradiction is resolved by there being two engineers, one the older and one the younger. I can't quite work out how to word the question to do it but I'm sure there is a way

Nyktos
Posts: 138
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### Re: Who is What?

SPACKlick wrote:I suspect the puzzle is trying to be a different puzzle entirely
Spoiler:
where we assume that all references to "The Engineer" and "The Programmer" can refer to any engineer/programmer rather than a specific one and that one of the brothers is both so what appears to be a contradiction is resolved by there being two engineers, one the older and one the younger. I can't quite work out how to word the question to do it but I'm sure there is a way
Spoiler:
This was kind of what I thought when I first saw the puzzle. Before actually trying to figure it out, my instinct was that the answer was going to be that the same brother was both an engineer and a programmer. "Software engineer" is a phrase that gets used, after all.

somehow
Posts: 99
Joined: Wed Aug 14, 2013 8:31 pm UTC

### Re: Who is What?

Nyktos wrote:
SPACKlick wrote:I suspect the puzzle is trying to be a different puzzle entirely
Spoiler:
where we assume that all references to "The Engineer" and "The Programmer" can refer to any engineer/programmer rather than a specific one and that one of the brothers is both so what appears to be a contradiction is resolved by there being two engineers, one the older and one the younger. I can't quite work out how to word the question to do it but I'm sure there is a way
Spoiler:
This was kind of what I thought when I first saw the puzzle. Before actually trying to figure it out, my instinct was that the answer was going to be that the same brother was both an engineer and a programmer. "Software engineer" is a phrase that gets used, after all.

If it's trying to be that sort of a puzzle, it's doing a strangely bad job of it, because

Spoiler:
the statement that "one is a programmer and the other is an engineer" seems to specifically rule out that sort of a tricky answer.
Xenomortis wrote:O(n2) takes on new meaning when trying to find pairs of socks in the morning.

SPACKlick
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Joined: Wed Apr 03, 2013 11:25 am UTC

### Re: Who is What?

somehow wrote:
Nyktos wrote:
SPACKlick wrote:I suspect the puzzle is trying to be a different puzzle entirely
Spoiler:
where we assume that all references to "The Engineer" and "The Programmer" can refer to any engineer/programmer rather than a specific one and that one of the brothers is both so what appears to be a contradiction is resolved by there being two engineers, one the older and one the younger. I can't quite work out how to word the question to do it but I'm sure there is a way
Spoiler:
This was kind of what I thought when I first saw the puzzle. Before actually trying to figure it out, my instinct was that the answer was going to be that the same brother was both an engineer and a programmer. "Software engineer" is a phrase that gets used, after all.

If it's trying to be that sort of a puzzle, it's doing a strangely bad job of it, because

Spoiler:
the statement that "one is a programmer and the other is an engineer" seems to specifically rule out that sort of a tricky answer.

Spoiler:
It doesn't rule it out at all If one is both and the other is either then that statement is true.

Cauchy
Posts: 602
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### Re: Who is What?

Use of the terms "the programmer" and "the engineer" later in the puzzle strongly (conclusively?) indicate that exactly one brother is a programmer, and exactly one brother is an engineer.
(∫|p|2)(∫|q|2) ≥ (∫|pq|)2
Thanks, skeptical scientist, for knowing symbols and giving them to me.

SPACKlick
Posts: 195
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### Re: Who is What?

Yeah but that's the sort of linguistic trick that logic puzzles use.

There are three words in the English language...

phlip
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### Re: Who is What?

I would strongly object to classifying any puzzle that used such a trick as a "logic puzzle".

Code: Select all

`enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}`
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SPACKlick
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### Re: Who is What?

I don't know. Implicit false assumptions are a logical trap appropriate to test in the real world. A puzzle based on reaching an apparent conclusion and then working out which assumption is made but unstated. I agree that the use of the is borderline deceitful and if I were creating the puzzle with one software engineer and one programmer I'd say "The engineer" and "The other's" and then try to avoid saying "the programmer".

phlip
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### Re: Who is What?

There's a difference between "implicit false assumptions" and "sentences that only make sense if you make false assumptions", such as a statement about "the engineer" would be if there were more than 1 engineer...

Code: Select all

`enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}`
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Cauchy
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### Re: Who is What?

If someone refers to "the engineer", and then it turns out that there were two engineers, that's not an implicit false assumption. You have actively lied to me through grammar in that case.
(∫|p|2)(∫|q|2) ≥ (∫|pq|)2
Thanks, skeptical scientist, for knowing symbols and giving them to me.