IOS>Settings>Restrictions>Passcode Wha ???

I had a problem with my iPhone. Somehow I had another password buried in my Settings. It caused a lot of problems, most notably it made the App Store App icon disappear keeping me from Updating any of my Apps.
There are two ways a Restrictions>Passcode is on your phone.
1. Your parents put it there to keep you from downloading expensive games from the App Store. This is not about that. or
2. You discover that  you can not get a new App or update an old App on you iPhone. Eventually you discover there's another password: known as Passcode in your settings. You have no idea how it got there. 

Apple would not allow me to post the following: (someone complained that 2014 this was still a not uncommon problem) [ added after Apple's rejection]
 

Feb 2016 IOS 9.2.1 Same problem is still going on.  Apple Care wasn't much help with Restrictions>Passcode. I finally figured out the sequence of events that leads to this mess. It's not your fault, it's not magic, it's not a bug--it's really just bad design. It's a trap.

First of all, kiddies who are trying to get around Restrictions? This doesn't apply. Your parents intentionally sought to use this to keep you out of trouble. They knew what they were doing when they setup the passcode. [psst: try grandma's birthday]
This is for the rest of us who stumbled into this: We are poking around the Settings investigating and learning. Probably those of us who uncheck the box "Please send me info every day, even better every five minutes!'
We see Restrictions. OK, what is this? We enter and we are immediately presented with a menu of stuff, and at the top it says, "Enable Restrictions" OK we're curious so we select the button and we are asked to enter a Passcode.
This key pad looks different than the one [you see] when you wake-up your phone. (I remembered it as being in a different order, like phones and calculators are different. It is not.) So you type in your PassWORD.  Mine is longer than 4 digits. This causes a problem, [but] as soon as you enter 4 digits the code is set and you go to the next step [no enter button to push, no moment of reflection]-you've just triggered the trap before you were aware something was different.   But you don't know this yet because you are looking at the lists of options that [seem like they will] should make your phone less intrusive: Push Notifications, Please Annoy Often and with strange noises, etc...  terrific. Good, [you think] I no longer want my phone to remind me in the middle of a meeting that I need to update Angry Toads...
But now [when you select some of the options for] the App Store[, it] disappears, along with the ability to update Apps when you select some of the options for it, [B]ut there is no way to know this until two weeks[, or two months] later when your Audible App stops working. You call for help, they tell you, update the app--but you can't find the App Store icon to do this..
Eventually you figure out it's this Restrictions thing and the Passcode is not your Password--You don't know what it is, because you don't remember setting it up. If it is the first four digits of your Pass[word]code you are in, and you are not reading this...
What happened to me is this turned out to be a variation of my password. I think the different key pad may be to alert you to the fact that you are now doing something different, maybe some people get it, those of us looking for help missed this too subtle tip. (I will not be a beta tester of the AppleCar. [everybody knows pressing the Home button parks the car, nobody presses the Home button when they're on the freeway....])
Apple Care told me that if I tried it 6 times and failed, it would lock my phone and I would have to Restore to New: lose information, my text messages and my mind.

This is not the case. After you fail for the 6th time, it just starts making you wait. First 1 minute. I got in on the 7th attempt, so I don't know what happens after that, but the best sources say 5 minutes, 15, 30 then 60 minutes. Some people report that they are on their 180th attempt, others that if you manually change the time on your phone you can just change the clock ahead and keep trying.

What I did. I made a list of the most likely numbers. First of all your Password, probably variations and [remember] only 4 digits--what do you sometimes mix up? If you are here reading this, you've already tried the first four digits of your password and it didn't work. Also we all have a couple of numbers we use for moderate security,  which if you are not trying to keep your kids out of trouble you might have used.
This Restrictions Passcode happens because it is one of those many areas in our digital world where as soon as you move on to the next step, you completely forget what just happened--the design of it almost guarantees this will happen. The less you know about Restrictions, the more likely you are to get in this mess.

I can tell you a number, then say 'remember it, I'll ask you for it later,'  I'll then change the subject. When I ask you five minutes later for the number you won't have a clue. It's why it's so easy to forget someone's name when you first meet.
Make the list, because as you get frustrated you will forget or doubt your accuracy. (This is why asking for a password once a week helps you remember it, but every fifteen minutes or every five minutes or every 10 seconds screws you up.) When you have your list, start working through it. If you first make a back-up to iTunes, after you get to the 30 minute waits, you can revert to the back-up. This should reset the Failed Attempts count, but I'm not sure. Restoring to a back-up, unless the Passcode is brand new, will not remove it.
I lost a full day and a lot of frustration because Apple Care scared me and I didn't want to risk that 6th attempt. I finally got through at the 7th.
This nonsense should not be happening to us 30 years into personal computing.<<end
Now is this so bad that Apple wouldn't allow me to share it with others?
Who's Big Brother now?