Newspaper puzzle

venda

Posers and Puzzles

28 Feb '21 18:33

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24 Apr '21 15:232 edits
@Shallow-Blue

I'm not talking about prime factors, although I suppose if you could get all the composite factors, you could get the prime factorization. I'm almost completely ignorant to how encryption works, I know it involves primes and have never given it more thought... I'm probably like most people, which is why it works I suppose. So you are saying that an formula to list out the factors of a number 𝑁 doesn't exist, and using a "cheat list" was the best way to solve this?
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24 Apr '21 15:55
@joe-shmo said
@Shallow-Blue

I'm not talking about prime factors, although I suppose if you could get all the composite factors, you could get the prime factorization. I'm almost completely ignorant to how encryption works, I know it involves primes and have never given it more thought... I'm probably like most people, which is why it works I suppose. So you are saying that an formula ...[text shortened]... ut the factors of a number 𝑁 doesn't exist, and using a "cheat list" was the best way to solve this?
All factors are either prime factors or compounds of prime factors. That's what the fundamental theorem of arithmetic means. If you can easily factor a number, you can easily find primes - and vice versa.

And yes, the only known way of doing so is doing the divisions and the divisions of the divisions. Which is easy for small numbers, but increasingly hard for large numbers; and that means that products of massive prime numbers play a role in cryptography. I know enough to know that, and I know just about enough to know that to explain it properly, I'd better refer you to Numberphile and Computerphile. If I tried to explain it myself, I'd get into an almighty muddle.
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25 Apr '21 05:37
@venda said
Which dials would be on zero if they only went up to 10?
Reveal Hidden Content
None.
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Dave
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25 Apr '21 09:48
@joe-shmo
Exactly right Joe
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25 Apr '21 09:49
@BigDoggProblem
Also correct
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Dave
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25 Apr '21 10:01
@shallow-blue said
All factors are either prime factors or compounds of prime factors. That's what the fundamental theorem of arithmetic means. If you can easily factor a number, you can easily find primes - and vice versa.

And yes, the only known way of doing so is doing the divisions and the divisions of the divisions. Which is easy for small numbers, but increasingly hard for large ...[text shortened]... to Numberphile and Computerphile. If I tried to explain it myself, I'd get into an almighty muddle.
I looked at public key cryptography once in relation to sending messages and as you say it's all to do with prime numbers.
venda
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02 May '21 09:361 edit
I don't have a lot of time for the forums at the moment,but I'll post this weeks newspaper puzzle for your amusement.It looks quite simple.I think it's just Venn diagrams:-
The Butchers ,Bakers and Candlestick makers union have merged into 1 union.The new union has (guess what!!)700 members.The butchers'union had 400 members.The Bakers' had 250 and the candlestick makers' 150.However there were 48 Butcher-Bakers,28 Butcher-Candlestick makers and 25 Baker-Candlestick makers.How can this all add up?
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02 May '21 12:513 edits
@venda said
I don't have a lot of time for the forums at the moment,but I'll post this weeks newspaper puzzle for your amusement.It looks quite simple.I think it's just Venn diagrams:-
The Butchers ,Bakers and Candlestick makers union have merged into 1 union.The new union has (guess what!!)700 members.The butchers'union had 400 members.The Bakers' had 250 and the candlestick makers' 150. ...[text shortened]... akers,28 Butcher-Candlestick makers and 25 Baker-Candlestick makers.How can this all add up?
Its not entirely clear what they are asking for, but

Reveal Hidden Content
There is 1 Butcher - Baker - Candlestick maker in the union
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Dave
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02 May '21 17:40
@joe-shmo
Correct Joe
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15 May '21 09:321 edit
I typed this out and as I was typing ,realised how easy it was but having gone to the trouble of typing it I thought I might as well leave it.
The queen threw all her regular six sided dice,added up the total and asked a citizen to roll that many dice and total their rolls.She then repeated this process for every citizen and the royal counter calculated that the average total thrown by the citizens was 7,007. what is the most likely number of dice in the Queens collection?
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16 May '21 14:573 edits
Reveal Hidden Content
I will have a go... most likely 572 dice in the queens collection
venda
Dave
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16 May '21 18:03
Correct Joe
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Dave
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23 Jun '21 18:042 edits
I don't know how to do this so I'll post it "word for "word" from the paper to avoid confusion.I'll also "hide" the answer as it's quoted:-
The Nootropian bar council has diversified it's membership.There are now Verists who always tell the truth.Mendists who always lie and Contrists who never lie or tell the truth twice in a row.The 700!! members are asked:-1.Are you a Verist.2.Are you a Contrist.3.Are you a Mendist.The total answering "yes" in each case is 500,200 and 50.[b]How is the council comprised[/b
Reveal Hidden Content
300 verists 150 mendists and 250 with 50 of the contrists starting off by lying and 200 starting off by telling the truth.Only contrists lying on questions 1 and 3 will answer "yes" to question 3.Only they and mendists will answer "yes" to question 2 and only they mendists and verists will answer "yes" to question 1
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05 Jul '21 09:34
@venda

Question Order: Are you a Verist? Are you a Contrist? Are you a Mendist?
Deduction of Answer Orders:
Verists
YNN

Mendists
YYN

Contrists
YYY T Y Contrist
YNY F
YYN F
YNN F
NYN F
NNY F
NYY F
NNN T N Contrist
Contrists answer all question as yeses or they answer all questions as nos.
I call Contrists with yes answers Y Contrists and Contrists with no answers N Contrists.

Further Deduction:
"Are you a Mendist?" gets 50 yeses. Only Mendists would say yes to this question. So 50 Y Contrists are here.
"Are you a Contrist?" gets 200 yeses. So 150 Mendists are here since only 50 Y Contrists would answer this question as yes (200-50=150).
"Are you a Verist??" gets 500 yeses. So 300 Verists are here since 50 Y Contrists and 150 Mendists would be a part of the 500 yeses (500-(150+50)=300)
So 200 N Contrists are here since 700-500=200.
So the council comprises of 300 Verists, 150 Mendists, and 250 Contrists.
venda
Dave
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05 Jul '21 12:33
@damionhonegan said
@venda

Question Order: Are you a Verist? Are you a Contrist? Are you a Mendist?
Deduction of Answer Orders:
Verists
YNN

Mendists
YYN

Contrists
YYY T Y Contrist
YNY F
YYN F
YNN F
NYN F
NNY F
NYY F
NNN T N Contrist
Contrists answer all question as yeses or they answer all questions as nos.
I call Contrists with yes answers Y Contrists and Contrist ...[text shortened]... e here since 700-500=200.
So the council comprises of 300 Verists, 150 Mendists, and 250 Contrists.
Correct.Well done!