Suppose we have to currencies, X and Y, and the rate of exchange between the two is R. Assume that everything is balanced, the rate is fair. On a given day, the central bank of currency X (unexpectedly) cuts the discount rate from 5.25% to 5%. Assuming everything else stays the same, by how much should Y appreciate against X? By 5% (5.25/5 = 1.05)?

You have the math all wrong. According to interest rate parity, with a surprise .25 cut in the discount rate, the currency value apppreciates by the amount of interest that is foregone, which is 0.25% over a year. For example, if the interest rate is cut from 5.25% to 5%. So the 1 year forward X/Y currency rate would be higher, implying that currency X would appreciate. It is counterintuitive that a lowering of the discount rate for currency X means that the currency should appreciate against currency Y. But that is interest rate parity, which prevents arbitrage. Theoretically, the dollar should be stronger in the future with lower discount rates. But in this world, theory and reality are very far apart, which is why everyone is saying the dollar will keep getting weaker even as the interest rates go lower.

If you mean by how much the fair value of Y changes against X then it depends on your formula for calculating the fair value of currency pair exchange rate. Just plug in the new rate in your formula and you'll get the new value of Y. If you mean the new market value of Y then only the market would know the answer. If the interest rate of currency X after the cut is still much higher than of currency Y the exchange rate might hardly move.

I looked it up at several web sites, and this is indeed what they say. But it doesn't make any sense to me. If two currencies A and B have the same interest rate, and then the interest rate for currency A goes up, wouldn't investors bid up currency A because it just became more attractive? I guess I am missing something major here.

There isnt such a thing as a "fair value" for currency exchange-rates. Like every other security, its price is determined according to supply and demand. High-yielding currencies usually appreciate in relation to low-yielding currencies, but this relation is not set in stone. Interest rates are only one of many factors that drive supply and demand. Its futile to try to predict the market in such simple terms ("if national bank cuts/raises interest for X spot-rate will do Y"). You can however of course accurately price forward and future contracts based on the spot rate (which is determined by "the market"), if you know maturity and the risk-free interest-rate (Libor).

I understand that. What I am trying to do is to figure out is the theory. According to the detective's post above and the web references, in interest rate parity, high-yielding currencies should depreciate. But according to your statement, and in all my experience, it's actually the opposite. That's what I am trying to reconcile.