I solved this brainteaser - can you? Any more like it for me?

[Hatshepsut]

My son gave me this brainteaser yesterday and I'm proud to say I solved it:

There are three cards placed face-down in front of you - one jack and two aces. You don't know which cards are which. You must pick a card but you don't get to see the face value.

Now you get to ask ONE yes-or-no question. If the card you picked was an ace, the question will be answered truthfully. If the card you picked was the jack, your question will be answered randomly - maybe truthfully, maybe with a lie.

What question do you ask so that when you get the answer you can correctly pick an ace out of the three cards?

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This reminds me a little bit of the "Let's Make a Deal" situation where people pick door #1, 2, or 3, and then Monty opens one of the doors that the contestant did not choose, revealing the dud behind. He then asks whether the person wants to change their pick. The correct choice is CHANGE TO THE OTHER DOOR. It doesn't mean you will win, but it does double your chances. This is very difficult for people to understand, but I'm happy to say it makes perfect sense to me, and I can even usually explain it to people so they get it too

Does anyone have more of these types of brainteasers for me? I'm in a logic-happy mood!

[CatInASuit]

Ok, I've been pondering it on and off for a while, so I will have a go.

No promises about even getting close.

It's probably something like, <pointing to a different card> would you tell the truth if I picked that card. If they say yes, you can pick the second card, because if your current card is an ace, then you have picked the other ace. If your current card is the jack, then the other two cards are aces and this time they answered truthfully. If they say no, then take the third card. If your current card is an ace then you have picked the jack. If your current card is a jack, then they have lied and the third card is still an ace.

[CatInASuit]

Ok, here's another brain teaser for you

Proof that 2 = 1, or maybe not.

                 a = b
               a*a = a*b                 (Multiply both sides by a)
         a*a + a*a = a*a + a*b           (adding a*a to each side)
a*a + a*a - 2*a*b  = a*a + a*b - 2*a*b   (Subtracting 2*a*b from both sides)
     2*a*a - 2*a*b = a*a - a*b           (Simplifying)
      2(a*a - a*b) = 1(a*a - a*b)        (Simplifying)
                 2 = 1                   (Dividing by (a*a - a*b))

So, what is the trick?