The coins roll down a ramp and fall through slots. The job requires having them move fast enough to skip over the slots that are too small and slow enough to fall into the slot if it is big enough...or are you on an electronics site because you want electricity to sort the coins? How about an optical slot in which light is detected to see how large the coins are?
Not "roll" down a ramp but slide flat, down a slope between guides that are just over 20mm apart. Then there's a hole in the surface that's 19mm across, so only the 25c coin can cross it, supported by opposite edges. The smaller coins fall through, and the process then repeats to separate the 10c and 5c coins. Easy. I've done it all for you.
It's a mechanical solution, not an electronic one.
The only electronic part would be adding an opto-interrupter to each "fall slot" to count the number of coins that fell in that tube, then multiply by the value of the coin that will fall into that tube.
Add totals from each tube to show total. If you want to get fancy, pause at each 40 or 50 coins (depending on thickness) so the tubes can be removed, coins put in to a roll, and process repeated.
~~If you pass the individual coins down a non-metallic chute, around which the coil of an oscillator is wound, the oscillator frequency will change. ~~Using a 80-100kHz oscillating field will allow good determination of different types of coins. By using filters the frequency associated with the value of each denomination of coin. ~~The chute should also have an optical component which detects the existence of a hole in a coin, which means it could likely detect washers used to defraud the user. ~~U.S. Patent No. 4,086,527 describes a similar technique with a variable frequency.
Slick sloped shutes with holes slightly smaller than coins so that all coins except largest coin will fall thru first shute hole, largest going down to pot. Second largest goes all the way down, dropping smaller ones on the way.
Some commercial choices. I think every kid should have one. My kids loved dropping their chore money in and watching it accumulate (albeit slowly - we didn't pay them much).