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I never doubted for a minute that you were correct, I just didn't think hard enough about it.
The difficult we do right away...
...the impossible takes slightly longer.
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Very interesting riddle, almost got a brain freeze  If you read carefully, the answer to get to 30 is quite obvious, unfortunately our brains are not wired that way.. 
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My first reaction, too. The first time I encountered this puzzle was an oral presentation. Made for some interesting notes, until one does the math correctly. The key is "where is the money", not "who spent what".
"A little time, a little trouble, your better day"
Badfinger
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Bringing QA experience to the Lounge!
"In testa che avete, Signor di Ceprano?"
-- Rigoletto
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Maybe - if you change "non-positive value" in your last sentence to "non-negative value".
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Oops!
Fixed
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony
"Common sense is so rare these days, it should be classified as a super power" - Random T-shirt
AntiTwitter: @DalekDave is now a follower!
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I'm not sure about your explanation, but I sense you are making the mistake I referred to yesterday, viz. basing your argument on the way number theory is implemented in the computer languages with which you are familiar, rather than on formal number theory itself. To answer the question we need the advice of pure mathemeticians on how magnitude of negative numbers is defined. How computers deal with it is clouded, as usual, by practicalities and compromise. However I doubt if there are any pure mathematicians lurking in this forum!
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Just as a side winder regarding the math's behind this, why is it that binary only runs on 0 (zero) and 1's with 0 being the neutral number then and not why use -1 0 0 1 1 0 -1 as binary.
Maybe I should just go Google first as this is above my paygrade... ?
And so I found this also relating to largest and smaller compared to bigger and less, sorry - Binary Negative Numbers![^]
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oh no this has prompted me to post for the first time ever...
> the general case is "if you add a positive number to a value, you get a value that is greater than the original"
That is your postulate, not a fact or proof. -1 is greater than -2 only if you assume this is true.
I propose another: To divide a quantity or object in half is to produce two halves that are each smaller than the original whole. Divide a number in half, the result is the smaller number.
> Let's look at what "greater than" actually means...
We all know language is ambiguous. It could actually mean many different things. Of course no one is arguing that (-1 > -2) doesn't evaluate to true in your programming language of choice*  That's just pragmatic.
*except maybe c++ in some cases...
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The formal mathematical proof that 1 + 1 = 2 runs to 360 pages of arcane symbols, and I don't understand a single page of it. I'm not going to try and modify that to formally prove X + n > X where n is a positive value because that proof would derive from 1 + 1 = 2.
Instead, I suggest you show any example which is consistent with 1 + 1 = 2 where X + n <= X where n is a positive value. If you are right and I am wrong (which I'm fully prepared to believe) it should be simple for you 
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony
"Common sense is so rare these days, it should be classified as a super power" - Random T-shirt
AntiTwitter: @DalekDave is now a follower!
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That is simple: you have a hole in the ground and add a positive amount of soil to it. Is the hole now bigger or smaller? The hole is negative volume.
Divide that hole in half, the half hole is smaller than the whole hole.
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tl;dr
"larger" is ambiguous
"larger" can mean "greater than"
"larger" can mean "greater magnitude than"
And that is the issue. English is fickle.
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They fixed my issue!
A most joyous day indeed!
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Maybe they noticed the message below. 
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So next time you contact MS Support, simply mention that you will post a rant on Codeprojekt about ms if the issue is not resolved within 24 hours
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Probably some Microsoft guys in the Lounge today.
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I think I've just invented some new swear words.
Over a month ago I got an email from Microsoft saying the Azure subscription of a customer wasn't paid.
I'd meet him that week so I'd ask about it, except the customer cancelled our meeting.
A week later already, Microsoft suspended the subscription.
Trying to log in to the subscription I found out I'd lost all access.
Somehow, two-factor authentication was enabled, but I don't have it in my phone, possibly because I'm a guest in the account and already have 2FA in other tenants?
I always have a back-up admin account, but at some point I must've changed the password without writing it down (I tried all my usual passwords, obviously).
I have a third account, but it isn't a global admin so it can't reset passwords and such and is useless in this particular case.
So far, my mistakes, must've been more careful with my accounts (although I'm fairly sure Microsoft just enabled 2FA one-sided, effectively locking me out).
So, two simple solutions: either disable 2FA on my account or reset the password of the back-up admin account.
It's taken over a month, four teams and a lot of emails and international calls with their heavy Indian accent support team and it still isn't fixed.
I've had to hand over a copy of my driver's license, a formal written request on company letterhead (who even has that!?) and a certificate of registration for my company.
That's basically me giving myself permission because I'm the only person in the tenant.
Haven't heard from them in over a week, despite my emails asking them to call me.
We're already past the point of resetting the password of the back-up admin account because it's a .onmicrosoft.com account with no email (they still emailed it TWICE though!).
Meanwhile, I've had the other issue of payment.
My customer's been without his software for weeks before I finally reached someone for payment!
So I made the payment and they continued on the issue of lost access.
Someone asked to look at my screen using quick assist, I showed him the problem, the accounts, and sent him screenshots as he requested.
Today I got a call telling me that person can't handle my issue because the ticket isn't assigned to his team and they don't do collaboration!?
WHY THE HELL DID HE EVEN CALL ME THEN!?
I'd have to create a new ticket, but I already have that ticket and they couldn't help me!
The sheer amount of incompetence is staggering!
JUST RESET MY ![Elephant | [mastadon]](https://www.codeproject.com/script/Forums/Images/elephant.gif) ING PASSWORD!!! 
If I'd treat my customers like this I'd be out of a job very soon.
If I never have to deal with Microsoft "support" anymore it'll be too soon!
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Welcome to business! 
Do you know why the payment stopped? Did your customer slip through the cracks or just forget?
As far as billing goes, it might be easier to bill your customers and you pay the hosting fees. Yes, it puts the burden on you to track it, report, etc. in QBO, but when it comes to supporting issues like this with a third party, you'll have to rely a lot less on other companies to figure out your customers' billing situation. You can also better control when service is stopped, etc. Of course, only do this with companies you trust to pay you.
Jeremy Falcon
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I avoid actual calls with MS like the plague.
Back in the early MSDN days, I had a boss who noticed that having a subscription entitled us to free support from MS, on basically any topic, so he encouraged us to call them. This predates Google (seriously, kids, there was a time when you couldn't just "google stuff").
I very, very quickly learned to avoid them at all costs.
My (current) boss called people from the MS Partner program a few months ago, since membership entitles you to some number of calls on any topic. So he did, discussing current business plans and inquiring about how to get there and the tools to use. After about a week, their emailed follow-up amounted to a dozen links that any half-trained monkey could've dug up.
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dandy72 wrote: This predates Google (seriously, kids, there was a time when you couldn't just "google stuff").
Oh yeah... going to the library to search for technical books and glancing / reading them to find information.
If you had luck, you had it on the first try or knew someone who would tell you which concrete book you needed. If you hadn't... you would spend a some hours over a couple of days to find it, if you ever found it.
Looking at how many waste and sponsoring links comes now in google searches... I start feeling the same way. 
M.D.V. 
If something has a solution... Why do we have to worry about?. If it has no solution... For what reason do we have to worry about?
Help me to understand what I'm saying, and I'll explain it better to you
Rating helpful answers is nice, but saying thanks can be even nicer.
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Maybe similar to back in the day when I used the encyclopedia to look something up. Hit Aardvark and got sidetracked.
Same with duckduckgo. Try to avoid Google.
>64
Itβs weird being the same age as old people.
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I do avoid google when I can
M.D.V. 
If something has a solution... Why do we have to worry about?. If it has no solution... For what reason do we have to worry about?
Help me to understand what I'm saying, and I'll explain it better to you
Rating helpful answers is nice, but saying thanks can be even nicer.
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There was of course the intermediate stage of having the MSDN CDs, which was almost the equivalent of having the entire MS knowledgebase. Almost, but not quite. At one stage I had getting on for 100 MS CDs (including demoes and trial versions) but finding stuff on that lot was a nightmare. And no, there wasn't room on my 256Mb disk to copy it all... π
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I have found some of the articles back then to still be interesting and worth reading.
There was an online archive with many of them... sadly there were a big bunch of linking errors and missing files.
M.D.V. 
If something has a solution... Why do we have to worry about?. If it has no solution... For what reason do we have to worry about?
Help me to understand what I'm saying, and I'll explain it better to you
Rating helpful answers is nice, but saying thanks can be even nicer.
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