There can only be an odd number of $50 bills, because if you had an even number of $50 bills, they would amount to $100, which would leave $410 to make with $20 bils only, which is impossible, or $200, which would leave $310 to make with $20 bils only, which is impossible, or $300, which would leave $210 to make with $20 bils only, which is impossible, or $400, which would leave $110 to make with $20 bils only, which is impossible, or $500, which would leave $10 to make with $20 bils only, which is impossible. But if you had an odd number of $50 bills, they would amount to 1. 1 fifty, or $50, which would leave $460 to make with $20 bills only, which can be made with 23 $20 bills. 2. 3 fifties, or $150, which would leave $360 to make with $20 bills only, which can be made with 18 $20 bills. 3. 5 fifties, or $250, which would leave $260 to make with $20 bills only, which can be made with 13 $20 bills. 4. 7 fifties, or $350, which would leave $160 to make with $20 bills only, which can be made with 8 $20 bills. 5. 9 fifties, or $450, which would leave $60 to make with $20 bills only, which can be made with 3 $20 bills. So there are 5 possible denominations of $20 and $50 that sum up to $510. Edwin