You don't HAVE to put any particular amount down, or even anything at all. It's just like buying any other house, getting a mortgage depends on your credit and what the property appraises for. Keep in mind that also sometimes a foreclosed home will sell for less than its listing price if there is little interest in it (although it might take some time for the bank to show any interest in a lower offer). It might also sell for MORE if the listing is significantly lower than market and the bank gets multiple offers that they allow people to revise until the highest offer is left.
If you're talking about trying to buy a property at the actual foreclosure sale at the courthouse (where the bank usually is the high bidder and legally obtains the title), you usually will have to have the full amount readily available, or an already established independent line of credit, as most states laws require at least a percentage right away, and the balance shortly thereafter. You can't be the high bidder at the foreclosure auction and THEN try to get a mortgage.
Professional appraiser/Gov't property analyst