#CallingAllMathematicians Please help with this math?

[DizzyDesii]

Okay so there are 8 numbers. Each column can only have 4 numbers. I need the total of the 2 columns to be as close to equal as possible. here's the numbers-
The 8 #s— 103, 97, 96, 75, 75, 73, 52, 46 Here’s the math I’ve done so far.
A
103+75+73+46=297
97+96+75+52=320
B
103+75+73+52=303
97+96+75+46=314
C
103+97+52+46=298
96+75+75+73=319
D
103+73+52+46=274
97+96+75+75=343
E
103+96+73+46=318
97+75+75+52=299
Is B as close to the same number as I’ll get or is there a combo I’m missing?

#FeelFreeToList

Updates

4 mo

OMG NEVERMIND I FINALLY FIGURED IT OUT! there's TOTALLY A CLOSER ANSWER THAN B 😩 TOOK ME AN HOUR LMAO

Updates

4 mo

Everyone did so great thank you! Special thanks to Alexefron for figuring out the above problem before anyone else and another Special thanks to Joshydavid for figuring out the second math problem listed below. (How to get 262 out of two rows using 7 numbers- 112 92 75 75 72 52 46)… I’ll try to remember to give y'all mho. I’ll also thank Nathandavis for having a different solution to avoid doing all of this math 🤣

[Joshydavid25]

Damn, I was actually gonna try and solve it but, as usual I got too curious and saw the other answers.. 😂.. Even though I'm far from a mathematician.. 😂..

[DizzyDesii]

Its okay i got a new one for you. Now its 7 numbers instead of 8. Which numbers belong in each column to get close to 262?
The 7#s 112 92 75 75 72 52 46

[Joshydavid25]

Hmmmm..

112+75+75=262
92+72+52+46=262..

[DizzyDesii]

Omgeeee thank you

[Joshydavid25]

No problem.. It was easier than I thought.. Thought I would be spending hours.
😂😂

[DizzyDesii]

Math was never my thing lol

[Joshydavid25]

Mine either.. That's why I was surprised.. Lol..

[Joshydavid25]

Thanks for MHO Des! 😁

[AlexEfron]

97+96+73+46 = 312

103+75+75+52 = 305

Difference = 7

[AlexEfron]

These are the kind of problems we need to solve in interviews 😂

[DizzyDesii]

Lol i’d get the job after the hour it took me to figure it out

[DizzyDesii]

Please explain to me how you figured it out so easily? What i did was added all 8 numbers, got 618 and divided by 2 so about 308/309. So all my combos were trying to get the totals as close to those as possible. But how did you figure it up so quickly?

[AlexEfron]

These seem deviously simple but it gets complicated with its variations. There are variants where you need to split the numbers in such a way that the sum is balanced (no restrictions on the number of numbers... you can have column 1 with only 1 number and column 2 with the rest). Then there's a variation with more columns. It gets progressively trickier 🥲.

[AlexEfron]

I'm a software engineer 🤣 I write programs. Even if I have to brute force all possible combinations, I'd write a 10-15 line script and get it answered in a couple of seconds 🤣. Besides, as I said, these are interview questions, so you will find a lot of software dev solutions out there

[DizzyDesii]

Oh wow

[AlexEfron]

And yes, that's the most optimal approach in my opinion. To make it easier - your total sum is 618 and you need your splits to be as close as 309. So you can start with the largest number (though I'd warn you... this is a nasty trap... choosing the largest number progressively is what we call a "greedy approach" which may give you "an answer" but not necessarily the "best answer") ...
Anyways
So initially the choice is 103 now add the next possible number... say the next largest is 97... so 103+97 (here's the greedy trap). You should consider 103+97, 103+96, 103+75... and then the third number and finally the 4th number. Whichever sum is nearest to 309 is the 4 from column 1 and the remainder is from column 2

[AlexEfron]

To give you another example... say you have bottles of capacity 1litre, 2litre, 5litre and 7litre. You're asked to package X litres of soda in as few bottles as possible. All bottles must be filled to the brim, you can't have a semi filled bottle. So suppose you're asked to package 20L. You can do 7+7+5+1 (4 bottles). Notice how I chose the largest bottles first. Now if someone asks for 10L, then following the same logic, I'd go 7+2+1 (3 bottles). Again the logic was choose the largest first and then the next largest 7,5 (but after filling the 7l bottle I have only 3L soda left and I can't have a half filled 5L bottle), so 7+2+1. But I skipped the possibility of 5+5 (only 2 bottles)

[DizzyDesii]

Thank you Professor

[DizzyDesii]

Now its 7 numbers instead of 8. Which numbers belong in each column to get close to 262?
The 7#s 112 92 75 75 72 52 46

[AlexEfron]

112+75+75=262
92+72+52+46=262

Who's asking you these? 😅

[DizzyDesii]

lol no one. I calculating prices

[AlexEfron]

😂 planning to buy something for Christmas?

[love_conquers_lust]

There’s ₈C₄/2=35 combinations you can try by hand. I used Excel Solver with Evolutionary Solving Method to get:

{97+96+73+46=312}-{103+75+75+52=305}=7

Listed out the numbers in a column. Set a binary constraint on a column next to the list of numbers. Set another constraint to sum those binaries to 4. I set the objective as the cell constaining formula:

617-SUMPRODUCT (range of numbers, range of binaries)

to a value of 0. It's a quick and dirty way without writing a custom brute force macro.

[DizzyDesii]

Holy smokes thanks

[RavVid]

Well I got 103+52+75+75 = 305 and 97+46+96+73 = 312 for a difference of 7 and slightly less than B.

I started by pairing the highest number available with the lowest number available to get two sets of 4 then cheated with Xcel to move numbers between columns. to get what seems to be the closest sum.

[DizzyDesii]

Yep thats correct. I went through all of that just to realize the numbers changed 😭🤦‍♀️ I should have used excel but i did it all on paper lol

[RavVid]

I'm too lazy to do it all on paper :) It is an interesting puzzle as there doesn't seem to be a generic way of doing it other than brute force number crunching.

[Oliverlogan263]

Ugh dude math sucks, I hate word problems. I don’t like math and math don’t like me lol. Let me think about this for a sec... Okay so from the combinations you have, E seems to be the closest with 318 and 299 right? I was never good at this kind of math stuff but thats what it looks like to me. Better than the other ones at least. You're right it does take forever to figure these kinds of things out! No wonder I dont want to do homework most of the time haha. Good job sticking with it though and figuring it out, at least you got there in the end!

[DizzyDesii]

Haha

[Oliverlogan263]

Lol 😂

[NathanDavis]

this is why I just pay the entire bill... lol

"enough, let's get out of here"

[DizzyDesii]

🤣🤣🤣 You already know

[NathanDavis]

lmao...

[DizzyDesii]

This is literally what this question is about lmao. I rather just pay cash but people wanna use their card so im havin to split shit 🤣

[NathanDavis]

if we ever go out... just let me charge it all to my work account, yes? lmao...

[DizzyDesii]

Such a sweetie pie 😩

[NathanDavis]

lol (=

[magiusX26]

nope. closest would be taking B and swapping the 46 and 52 leaving you with a difference of 3 between the 2 totals

[magiusX26]

scratch that. was only doing minor adjustments in my head and not checking my work.

[DizzyDesii]

I think you got it

[magiusX26]

that was about 10 or 15 mins while doing something else, rough estimating what was closest to each other as totals

[DizzyDesii]

Yea took me an hour earlier today just to get the correct answer

[nawtee_me]

Take A and swap 73, 46 with 75, 52. Making 305 and 312

[DizzyDesii]

Yea i figured that out. But i need help with one more. Now its 7 numbers instead of 8. Which nunbers belong in each column to get close to 262?
The 7#s 112 92 75 75 72 52 46

[electromagnetic]

First I was gonna say 7 because that’s everyone’s lucky number. Then I decided to be smart and look at the comments.
Girl, math wasn’t it for me.

[DizzyDesii]

Lmao you're not alone

[abc3643]

What class is this?

What is the answer?

I am fascinated by this question.

[DizzyDesii]

Lol its more so about splitting costs

[abc3643]

I got:

COLUMN 1:
103
75
75
52
SUM_1 = 305

COLUMN 2:
97
76
73
46
SUM_2 = 312

DIFFERENCE:
ABS (SUM_2 - SUM_1) = 7

Is that what you got?
If so, then I will describe how I got it fairly quickly.

[DizzyDesii]

Please explain how you got it quickly. Do you have some smart calculate with an Abs button or something? Lol

[abc3643]

ABS means absolute value. That's just the number without the sign. So, ABS (-1) = 1 and ABS (1) = 1.

I used my head and a spreadsheet to do quick additions.

I will explain more later. Sorry, but I have to go back to work...

[abc3643]

[abc3643]

OK, here's the story.

In this spreadsheet, we see the 8 numbers you gave us in Column A.
I wanted to compute the average of those numbers and then "shift the mean" (the term "mean" is the same as "average"; statistics professionals say "mean").
When you shift the mean, it often helps make visualizing and understanding how to attack a problem much easier. And it definitely helped here...

So, the difference from the mean is given in Column B.
We'll use this in a bit...

OK, the first way to try and solve this quickly is what the sports world does with a playoff bracket...
In a 4-team playoff bracket, the #1 team plays the #4 team and the #2 team plays the #3 team. This way, it's balanced as best as it can be with competitiveness.
In an 8-team playoff bracket, sort of like this, #1 plays #8, #2 plays #7, etc.
So, with your numbers, 103 is #1 and #46 is #8, etc.
So, a good first guess would be:
First Column:
#1, #8, #2, #7
Second Column:
#3, #6, #4, #5
So, that would be, sorting high to low:
1st: 103, 97, 52, 46
2nd: 96, 75, 75, 73
That gets us in the ballpark, but there are other sports bracket ways we could have done this, but I will skip those.

(more)

[abc3643]

OK, the second method is what I call "Collecting Zero Sums".
Remember that Column B with the deviations from the mean (aka "distance from the average")?
Look at the numbers closely... We have 3 numbers > 0 and 5 numbers < 0, but they themselves add up to be 0 and that should make sense. If the average of a group of numbers is Z then the average deviation from Z is 0.
Some things immediately stand out.
103 is 25.875 above the mean but 52 is -25.125 which is below the mean.
We are going to want to "collect this zero sum". They sum to 0.625, but that's close.
Now, lets look at another grouping...
97 is 19.875 above the mean and 96 is 18.875. Totalling about 39 above the mean.
But that 46 is already 31.125 below the mean. So, since we have 3 numbers there: 97, 96, 46 but we can only have 4 in a column, we now need another number that can get us as close to 39 as possible. That's the 73 which is -4.125.
So, 97, 96, 73, 46 are, collectively...
19.875+18.875-31.125-4.125=3.5
That's pretty close to 0 too.
So, that leaves us with those two leftover 75s. We'll put them in the first group with the 103 and 52.
So, 103, 52, 75, 75 are, collectively...
25.875-25.125-2.125-2.125=-3.5
That will give us a difference of (3.5)-(-3.5)=7 in the end.

(more)

[abc3643]

Don't get hung up on all this arithmetic.
I didn't do it.
What I did to get the answer quickly was to "shift the mean"... so I'd look at the numbers with the average now being the "new zero". Again, this is very common to do when solving mathematics and engineering problems.
Once I shifted the mean and saw the differences between each number and the average, it was obvious which collections of numbers immediately "zeroed each other out". The 103 and 52 were striking. So were the 97, 96, 46, and that the rest were small. It was the second grouping that would define a column and then the other column would be the remaining 4.

I am not expecting you to fully understand this and, honestly, I am winging this explanation, but try to take away this idea of "shifting the mean". It makes the math easier to visualize and it enabled me to realize what had to be done right away.

A good real world example of shifting the mean is golf. While in golf, the total strokes are what matter, golf has "par" for each hole. This is like an average. As the golfers play, we say a player is so many strokes "over par" or "under par". This way, was can see how players are ranking against each other on any day even though players may be many holes apart so their total strokes are very different until both players are done and played all the holes.

[DizzyDesii]

Holyyyyy guacamole! Thank you. I hope you get superb but i already agreed to give mho to the two who figured it out first. This was very helpful

[abc3643]

I wanted to mention something...

With the "collecting zero sums" method, I am trying to make each numbers (*) in each column sum to 0.

(*) The "shift the mean" numbers

Since the total sum of ALL 8 numbers in this method is 0, the sum in one of the columns with be -1 * the sum of all the numbers in the other column.

This is why you see in the two examples in someone - Q = - (SUM2 - Q)

[DJB72]

You're making my head spin

And not in the fun way...

[DizzyDesii]

Lmao

[MysticDevice]

Good lord. Glad you figured it out cause my brain would have torn a hole between dimensions trying to figure that out

[DizzyDesii]

I know it took forever 😩 I sent this to everyone in my phone and they’re all still tryna figure it out but i finally got it 🤣

[Phoenix98]

Sorry I looked at the first line and my brain just shut down.

[DizzyDesii]

🤣🤣

[Phoenix98]

Yeah math and me don't mix.

[Sparkie460]

I'm glad you figured it out. My brain would be smoking if I tried figuring it out

[DizzyDesii]

I sent it to everyone in my phone and they’re still at it. It took me an hour to get it

[Sparkie460]

I'd probably be just like everyone else you sent it to.

[SunnyRS]

305 and 312?

[DizzyDesii]

Yea but how did you get it so quickly

[SunnyRS]

Nothing much I just tried to make bundles.
Like 75+75 would make 150.
And 73 and 97 would make 170.
Like that.
And now I know you will ask then why not 103 and 97?
It's because it will make one bunch too bigger with just two numbers.

[DizzyDesii]

So why 73 and 97 before 73 and 96

[SunnyRS]

Because 73 and 96 don't make bundle.
You know a bundle means a combination of numbers ending with zero.

[DizzyDesii]

The teachers here never explained that 😂

[SunnyRS]

It's a simple thing but it doesn't always work. It just makes addition easier. So many teachers don't explain it.
Sorry wifey if it sounded like I was mansplaining, that was not my intent here.

[DizzyDesii]

No you didn't you explained perfectly

[SunnyRS]

Good wifey.
*Pat on the head

[DizzyDesii]

Now its 7 numbers instead of 8. Which numbers belong in each column to get close to 262?
The 7#s 112 92 75 75 72 52 46

[SunnyRS]

We have to make two sets like earlier?
And both should be near 262?

[SunnyRS]

In two sets we can get 262 it is not necessary to get close.
One set- 75+75+112=262
Second set- 92+72+52+46=262

[SunnyRS]

I hope that was the question

[DizzyDesii]

Yes that was! Thank you 🙏

[SunnyRS]

Ok 👍

[FenixG45]

No Problemo! Anytime! It was NOTHING at all!

[DizzyDesii]

Lmao did you actually try to do it? Just curious

[FenixG45]

Ummmm... whose asking?

[SimplyPut]

Have three columns

[DizzyDesii]

Its split between 2 people

[SimplyPut]

Well ok

[sirderpsalot123]

🤯🤯🤯

[DizzyDesii]

Lmao

[LunarEclipse433]

E is a lot closer

[DizzyDesii]

So E is like 309-299=10, 318-309=9.
But if i do 312-309=3 and 309-305=4.
Thats closer

[LunarEclipse433]

No I am wrong. I read one of the answers incorrectly

[DizzyDesii]

You were close tho