I had a deck of cards but I lost a few. When I play with 3 other people, I have three cards left. When I play with 2 other people 2 cards are left. When I play with 4 other people, I have 2 cards left. How many cards have I lost?
let the number of cards left in the deck be NN(mod4)=3N(mod3)=2N(mod5)=2N≈52, N<52
N=4k+34k+3(mod3)=2k+(3k+3)(mod3)=2k(mod3)=2k=3j+2N=12j+1112j+11(mod5)=22j+1+(10j+10)(mod5)=22j+1(mod5)=22j(mod5)=12j(mod5)=6j(mod5)=3j=5i+3N=60i+36+11=60i+47N=47
