Random Thoughts Part 5: Time to Split Again

[Sophia]

allright. I am neither a child nor a genius. Was reading wikipage about Voyager and found this

what the heck those horizontal and vertical lines mean? Hopefully our extraterrestrial friends are much smarter than me :)

 

[Enigman]

allright. I am neither a child nor a genius. Was reading wikipage about Voyager and found this

what the heck those horizontal and vertical lines mean? Hopefully our extraterrestrial friends are much smarter than me :)

Binary. Dashes are zeroes and l's are ones.

 

[Enigman]

What is the beginning of eternity, the end of time and space, the start of every end, and the end of every race?

 

[Sophia]

Binary. Dashes are zeroes and l's are ones.

ooooh!
That would never come to my mind even if I stared at it for years ) I assumed it was something that could be understood intuitively, like the dots.

 

[Ibix]

Binary, with the dash standing in for zero.

Edit: beaten to it by Enigman. Although none of those posts were there when I posted this one.

 

[Ibix]

What is the beginning of eternity, the end of time and space, the start of every end, and the end of every race?

It's a mystery. Like your old avatar.

 

[WWGD]

I was reading on how one learns by listening, not by talking. But then if everyone follows this, no one will talk
and there will be nothing to listen to, to learn from...

 

[Psinter]

Here, one usually rounds to the nearest 50 cent or euro at an average pub, pizzeria or delivery fast food. If you go to a proper dinner, than it's usually rounded to 5 or 10 euro.

You have euro too?! I have one and I like it, it looks cool. I have one coin that says "1 EURO Liberté Égalité Fraternité" and has a tree. No idea what it means, but it rhymes. And it looks awesome. It's like a central disc of color silver and an outer ring of color gold.

I also have one that says "Two Pounds, Elizabeth II Dei Gra Reg Fid Def". Also no idea what it means, but it's cool.

I also have one that says "1 Cent Canada, Elizabeth II D G Regina".

 

[Sophia]

You have euro too?! I have one and I like it, it looks cool. I have one coin that says "1 EURO Liberté Égalité Fraternité" and has a tree. No idea what it means, but it rhymes. And it looks awesome. It's like a central disc of color silver and an outer ring of color gold.

Yes, that's French version of euro coin. They all look the same on the front side and each country puts their own symbols on the back side (you can pay with any of them in all Euro countries)
Liberté Égalité Fraternité means "liberty, equality, brotherhood" and it comes from the French revolution https://en.wikipedia.org/wiki/French_Revolution
I like euro money, I think it's very nice and distinct colours of banknotes make it easy for people with visual impairment to distinguish between them. The only downside are small cent coins which are almost universally hated and bear almost no value.

I also have one that says "Two Pounds, Elizabeth II Dei Gra Reg Fid Def". Also no idea what it means, but it's cool.

I also have one that says "1 Cent Canada, Elizabeth II D G Regina".

let's leave that to our Commonwealth friends to explain

 

[Psinter]

Yes, that's French version of euro coin. They all look the same on the front side and each country puts their own symbols on the back side (you can pay with any of them in all Euro countries)
Liberté Égalité Fraternité means "liberty, equality, brotherhood" and it comes from the French revolution https://en.wikipedia.org/wiki/French_Revolution
I like euro money, I think it's very nice and distinct colours of banknotes make it easy for people with visual impairment to distinguish between them. The only downside are small cent coins which are almost universally hated and bear almost no value.

Nice. I learned something today.

 

[Pepper Mint]

But European countries have different living standards, how can they cope with them if they use the same currency like that ?

 

[Sophia]

But European countries have different living standards, how can they cope with them if they use the same currency like that ?

There are certain standards a country must meet if they want to adopt euro. They concern state budget and debt. Don't ask me about details, I have no idea what they are. Then there is Central European Bank that regulates inflation https://www.ecb.europa.eu/home/html/index.en.html
There are of course problems, like with Greece which has incredible state debt and other countries had to help them. There was a negative attitude towards the help in Slovakia, because we managed to decrease our national debt and the GDP is rising constantly, but we had to borrow a large amount of money for high interest (compared to our economy) in order to send that money to Greece while our own social and healthcare system needs help. But it was inevitable, otherwise there would be huge problems in the eurozone.

 

[WWGD]

There are certain standards a country must meet if they want to adopt euro. They concern state budget and debt. Don't ask me about details, I have no idea what they are. Then there is Central European Bank that regulates inflation https://www.ecb.europa.eu/home/html/index.en.html
There are of course problems, like with Greece which has incredible state debt and other countries had to help them. There was a negative attitude towards the help in Slovakia, because we managed to decrease our national debt and the GDP is rising constantly, but we had to borrow a large amount of money for high interest (compared to our economy) in order to send that money to Greece while our own social and healthcare system needs help. But it was inevitable, otherwise there would be huge problems in the eurozone.

Yes, it kind of sucks, but a common market may be the only way to prevent a WW3 by making people feel they are in it together.

 

[Sophia]

Yes, it kind of sucks, but a common market may be the only way to prevent a WW3 by making people feel they are in it together.

Yes, I agree. Though I think it will be much more difficult to create something like the USA in Europe. There is too much history, too much emotions to cope with.

 

[OmCheeto]

ooooh!
That would never come to my mind even if I stared at it for years ) I assumed it was something that could be understood intuitively, like the dots.

This puzzle should be much easier for you than for Americans.

I had to be shown the answer...
And then I was like; "Oh. That's right. You have to sometimes think outside of the box, in more ways than one."

 

[Ibix]

This puzzle should be much easier for you than for Americans.

View attachment 97634

I had to be shown the answer...
And then I was like; "Oh. That's right. You have to sometimes think outside of the box, in more ways than one."

I can think of two ways to do it - one is definitely cheating.

Spoiler

Leave the first box blank and use 15 in the others: +15+15=30

Spoiler

Turn the nine upside down to make a six. Then 6+11+13=30

 

[Sophia]

This puzzle should be much easier for you than for Americans.

View attachment 97634

I had to be shown the answer...
And then I was like; "Oh. That's right. You have to sometimes think outside of the box, in more ways than one."

I thought of leaving one box blank, too 15+15= 30

or putting more numbers in one box
(15-5)+(15-5)+(15-5)= 30

 

[Ibix]

or putting more numbers in one box
(15-5)+(15-5)+(15-5)= 30

Didn't think of that. You can generalise it - (11-1) and (13-3) also work.

Also, 15+15+1 works if we're using base 11 (because 15 read in base 11 is 16 in base 10, and 30 read in base 11 is 33 in base 10).

 

[zoobyshoe]

I had to be shown the answer...
And then I was like; "Oh. That's right. You have to sometimes think outside of the box, in more ways than one."

I have the feeling any "answer" that works actually violates implied constraints.

 

[Borg]

I have the feeling any "answer" that works actually violates implied constraints.

Yes, I don't see how you can add three odd numbers to get an even answer without some sort of trick answer.

 

[zoobyshoe]

Yes, I don't see how you can add three odd numbers to get an even answer without some sort of trick answer.

And the problem with that is: the person confirming or denying your answer can decide which kind of "trick" is allowed and which isn't.

 

[OmCheeto]

I have the feeling any "answer" that works actually violates implied constraints.

The only constraints I see are:

1. Fill the boxes
2 using: (1,3,5,7,9,11,13,15)​

And then there's the "unconstraint":

1. You can also repeat the numbers​

 

[zoobyshoe]

The only constraints I see are:

1. Fill the boxes
2 using: (1,3,5,7,9,11,13,15)​

And then there's the "unconstraint":

1. You can also repeat the numbers​

What are the implied constraints, though?

 

[Ibix]

I looked it up and came across the following, which I suspect is the particular trick they were after:

Spoiler

3(+1+9)=30

It's still a trick. I prefer my base-11 solution.

 

[collinsmark]

The only constraints I see are:

1. Fill the boxes
2 using: (1,3,5,7,9,11,13,15)​

Agreed.

Unfortunately, I believe the answer for which they are looking violates constraint #1. [Edit: Oh, I get it, the parentheses, "(" and ")" were included in the list of possible choices to use, allowing a different solution. But that's also silly. Not only does that answer misuse an instance of the addition operator, the parentheses characters were not properly delimited within the list of choices.]

That is why I have more appreciation for @Ibix's answer of changing from base 10 to a different base. It gives an answer that satisfies the equality without violating any of the constraints. Unfortunately, I doubt that was the answer the author of the problem deemed correct.

And then there's the "unconstraint":

1. You can also repeat the numbers​

And for that, I'm guessing that the author really meant to say, "You may also repeat the numbers." The grammatical error increases the ambiguity of the problem.

 

[OmCheeto]

What are the implied constraints, though?

As far as I can tell, there are no implied constraints.
Do what you have to do, with the "given".

I believe that my best clue was; "This puzzle should be much easier for you than for Americans."
Sophia is European.

 

[zoobyshoe]

As far as I can tell, there are no implied constraints.
Do what you have to do, with the "given".

There are many obvious implied constraints they haven't addressed: one number per box (no arithmetical operations), no alteration of numbers by the addition of factorial signs, plus or minus signs, "approximately equal to" signs, radicals, all that, each box must be used (no box may be left empty), and, there is the implied constraint to use of base ten. I'm sure there are others I haven't thought of.

By singling out one constraint, the possible assumption that a number may only be used once, and releasing you from that constraint, they have implied that they have addressed all the implied constraints you need to discard, which is quite misleading.

 

[OmCheeto]

ps. I loved this problem so much, that I threw it out on Facebook.
So far, it's even kickin' you know who's butt.

Tom Mattson

Simply adding 3 odd numbers will produce an odd number, so other operations have to be allowed so as to introduce even numbers. Right off the bat I can see 2 ways to do this.

1.) Use a factorial. Specifically: 3! = 6.
So I have 3! + 9 + 15 = 30.

2.) Use Euler's totient function. If n is a positive integer, then Euler's totient function f(n) counts the number of positive integers that are less than n and that are relatively prime to n. Specifically: f(11) = 10. So I have f(11) + f(11) + f(11) = 30.​

 

[OmCheeto]

...implied constraints they haven't addressed: one number per box...

And that "thinking inside of the box" may give it away...



I laughed at myself, most heartily, when I saw the answer.

ps. Ibix's answer, had he thought outside of the box, would have been most correct, IMHO.

 

[zoobyshoe]

I looked it up and came across the following, which I suspect is the particular trick they were after:

Spoiler

3(+1+9)=30

It's still a trick. I prefer my base-11 solution.

If what's in your spoiler is the alleged "right" answer then:

And the problem with that is: the person confirming or denying your answer can decide which kind of "trick" is allowed and which isn't.

 

[OmCheeto]

I have the feeling any "answer" that works actually violates implied constraints.

Borek came up with one that didn't violate any constraints; "You want me to get creative? If you write 3 twice in the same place, rotating it 180 deg for the second copy, you get 8. 11+11+8=30."

As the kids nowadays say; "BAM!"

Oh wait. That may have been totally, a last week term.

 

[collinsmark]

There's another solution exploiting commas in the list of possible symbols (to fill the boxes).

Specifically, in some cultures the comma is used to indicate the decimal point. For example, "4,5" is four and a half under this convention. One could use this to create a valid answer.

Maybe that what what @OmCheeto's previous hint was about?

 

[OmCheeto]

There's another solution exploiting commas in the list of possible symbols (to fill the boxes).

Specifically, in some cultures the comma is used to indicate the decimal point. For example, "4,5" is four and a half under this convention. One could use this to create a valid answer.

Maybe that what what @OmCheeto's previous hint about European vs. American?

Jerk...

 

[NascentOxygen]

I think base 5 works.

But perhaps it intends that you should use all of the numbers supplied?
e.g., (15-5) + (13-3) + (11+9-7-1-1-1) = 30

 

[Ibix]

I think base 5 works.

How do you interpret 5, 7, 9 and 15 in that case?