Random Thoughts Part 5: Time to Split Again

[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?

 

[NascentOxygen]

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

The base 5 solution doesn't make use of those symbols.

 

[Ibix]

The base 5 solution doesn't use those.

I'd like to see a base 5 solution that did. But my point is that if you read the numbers in base 5 they aren't even valid symbols, so either have to be discarded as garbage or read in another base. That's why I went for a base greater than nine.

Given the range of creative solutions we've come up with, I suppose it's not a major issue.

 

[zoobyshoe]

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!"

The kids should be saying,"Obvious violation of implied constraints."

Your statement, "Borek came up with one that didn't violate any constraints" is just plain not true.

 

[OmCheeto]

The kids should be saying,"Obvious violation of implied constraints."

Your statement, "Borek came up with one that didn't violate any constraints" is just plain not true.

You seem to be hung up on "implied" constraints.

I think they are all in your head.

 

[zoobyshoe]

You seem to be hung up on "implied" constraints.

I think they are all in your head.

I don't think they are. Try creating an 8 from two threes in some other situation and see how accurate your answer is. There's such an obvious implied constraint against that that no one would seriously consider it.

 

[OmCheeto]

I don't think they are. Try creating an 8 from two threes in some other situation and see how accurate your answer is. There's such an obvious implied constraint against that that no one would seriously consider it.

To be honest, I don't know what the official answer is. But I do know a bit of maths, and a few of the rules, so I decided to be the judge of the answers.
And after my nap, I decided the there are, as you mentioned, some implied constraints.
The last two sentences were obviously added after the fact, and should be ignored completely.
I also decided that the quiz was done with a pencil, so Borek's merger of two 3s seemed legitimate.

The answer I saw was [15] + [11,3] + [3,7]
This is why I called collinsmark a jerk, as I thought it was too big of a hint.
Commas are used as decimal points in Europe, South America, and Western Africa. [ref]

The Ibix & Sophia solution that I considered correct was: [ , ] + [15] + [15]
although they said they were cheating by leaving a box blank.
But the instructions don't tell you to use the numbers, so putting a comma in one of the boxes works fine, IMHO.

I also like the base change solutions, but that might lead to an ungodly number of solutions.
[ 5₁₅ ] + [ 7₁₅ ] + [ 9₁₅ ] = 30₇
I'm guessing it falls under the pattern:
[ x ] + [ y ] + [ z ] = w_base
where w = 3 * base

The most trivial ones I saw were:

[ 5₇ ] + [ 5₇ ] + [ 5₇ ] = 30₅
[ 7₁₅ ] + [ 7₁₅ ] + [ 7₁₅ ] = 30₇
etc, etc.

But I do understand your "implied constraints" now, as, you can be most creative, without them:

 

[OmCheeto]

ps. About a year before I retired, my company fired me from my management position.
But they kept me on, as a sort of consultant.
So I got to sit in my new boss's office, with my new boss, for about a year, in what used to be my office.
Sometime very near my retirement date, he blurted out something to the effect; "Do I really need to make a new policy rule to cover this"?
I told him; "There are already too many rules. I've been here for 30 years, and every time there's a problem, a new rule gets posted. Eventually, the only rule left will be; "Don't poop on the floor." At which point, someone will pee in the corner."

true story

 

[NascentOxygen]

In some fonts the parentheses wrap-around like a semicircle, so if you type three consecutive characters 3() it forms what resembles 30.

 

[OmCheeto]

In some fonts the parentheses wrap-around like a semicircle, so if you type three consecutive characters 3() it forms what resembles 30.

[ , ] + [ , ] + [ 3() ] = 30

I accept your answer!

Good one!

 

[NascentOxygen]

The answer I saw was [15] + [11,3] + [3,7]

I can see how that may be construed, but I wouldn't allow it, there not being an "11,3" or "3,7" pattern evident in the given set.

I would accept 7,9 + 9,1 + 13 as these sequences of characters are, arguably, all present.

 

[NascentOxygen]

[ , ] + [ , ] + [ 3() ] = 30

Not quite. I meant you could regard "+" as a string concatenation operation, as in BASIC,
[ 3 ] + [ ( ] + [ ) ] = 3()

 

[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."

What about turning it into equation?
3x+5+7=30

This would give us nice number 6

Or another option
15+9+7=30+1

 

[Psinter]

I told him; "There are already too many rules. I've been here for 30 years, and every time there's a problem, a new rule gets posted. Eventually, the only rule left will be; "Don't poop on the floor." At which point, someone will pee in the corner."

What does that mean (if anything)? I don't understand.

 

[Sophia]

Spring is here! (spring equinox)

and something for Psinter

Spoiler

 

[einswine]

What does that mean (if anything)? I don't understand.

I think it means that once one has had to create a rule for every stupid thing you can image someone will do, they will figure out something even stupiderer than that.