You have pennies (1c), nickels (5c), dimes(10c), quarters (25c), and half-dollars (50). Solve the following problems:

a) Choose a combination of exactly 100 coins such that the total sum is exactly $5. There must be at least one of each coin.

b) Choose a combination of exactly 100 coins such that the total sum is exactly $5. There must be at least two of each coin.

c) Choose a combination of exactly 100 coins such that the total sum is exactly $5. There must be at least three of each coin.

d) Choose a combination of exactly 100 coins such that the total sum is exactly $10. There must be at least one of each coin.

Note: For some of the problems, there are multiple possible solutions. It is possible to arrive at a solution by trial and error. However, the ideal way of solving this exercise is to discover a method to solve all the above problems in a less tedious manner than trial and error. =)

a) Choose a combination of exactly 100 coins such that the total sum is exactly $5. There must be at least one of each coin.

b) Choose a combination of exactly 100 coins such that the total sum is exactly $5. There must be at least two of each coin.

c) Choose a combination of exactly 100 coins such that the total sum is exactly $5. There must be at least three of each coin.

d) Choose a combination of exactly 100 coins such that the total sum is exactly $10. There must be at least one of each coin.

Note: For some of the problems, there are multiple possible solutions. It is possible to arrive at a solution by trial and error. However, the ideal way of solving this exercise is to discover a method to solve all the above problems in a less tedious manner than trial and error. =)

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