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49 without using the fifty-cent piece listed below 1... H

2... 2Q

3... Q,2D,1N

4... Q,2D,5P

5... Q,1D,3N

6... Q,1D,2N,5P

7... Q,1D,1N,10P

8... Q,1D,15P

9... Q,5N

10 Q,4N,5P

11 Q,3N,10P

12 Q,2N.15P

13 Q,1N,20P

14 Q,25P

15 5D

16 4D,2N

17 4D,1N,5P

18 4D,10P

19 3D,4N

20 3D,3N,5P

21 3D,2N,10P

22 3D,1N,15P

23 3D,20P

24 2D,6N

25 2D,5N,5P

26 2D,4N,10P

27 2D,3N,15P

28 2D,2N,20P

29 2D,1N,25P

30 2D,30P

31 1D,8N

32 1D,7N,5P

33 1D,6N,10P

34 1D,5N,15P

35 1D,4N,20P

36 1D,3N,25P

37 1D,2N,30P

38 1D,1N,35P

39 1D,40P

40 10N

41 9N,5P

42 8N,10P

43 7N,15P

44 6N,20P

45 5N,25P

46 4N,30P

47 3N,35P

48 2N,40P

49 1N,45P

50 50P
49 Without using fifty-cent piece which has been included in the list below. 1.. H

2.. 2Q

3.. Q,2D,1N

4.. Q,2D,5P

5.. Q,1D,3N

6.. Q,1D,2N,5P

7.. Q,1D,1N,10P

8.. Q,1D,15P

9.. Q,5N

10 Q,4N,5P

11 Q,3N,10P

12 Q,2N.15P

13 Q,1N,20P

14 Q,25P

15 5D

16 4D,2N

17 4D,1N,5P

18 4D,10P

19 3D,4N

20 3D,3N,5P

21 3D,2N,10P

22 3D,1N,15P

23 3D,20P

24 2D,6N

25 2D,5N,5P

26 2D,4N,10P

27 2D,3N,15P

28 2D,2N,20P

29 2D,1N,25P

30 2D,30P

31 1D,8N

32 1D,7N,5P

33 1D,6N,10P

34 1D,5N,15P

35 1D,4N,20P

36 1D,3N,25P

37 1D,2N,30P

38 1D,1N,35P

39 1D,40P

40 10N

41 9N,5P

42 8N,10P

43 7N,15P

44 6N,20P

45 5N,25P

46 4N,30P

47 3N,35P

48 2N,40P

49 1N,45P

50 50P

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Q: How many ways can you make change for fifty cents using quarters nickels dimes and pennies?
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The minimum number of quarters, pennies, and nickels needed to make up 123 cents is 4 quarters, 4 nickels, and 3 pennies.


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