It depends on what you mean by height - are the coins stacked or arranged side by side?
If they're side by side, the dimension is 6*21.21 mm = 127.26 mm
If they're stacked, the dimension is 6*1.95 mm = 11.70 mm
There are 19 different ways to make 36 cents. 1 quarter, 1 dime, 1 penny 1 quarter, 2 nickels, 1 penny 1 quarter, 1 nickel, 6 pennies 3 dimes, 1 nickel, 1 penny 2 dimes, 3 nickels, 1 penny 2 dimes, 2 nickels, 6 pennies 2 dimes, 1 nickels, 11 pennies 1 dime, 4 nickels, 1 nickel, 1 penny 1 dime, 3 nickels, 11 pennies 1 dime, 2 nickels, 16 pennies 1 dime, 1 nickel, 21 pennies 7 nickels, 1 penny 6 nickels, 6 pennies 5 nickels, 11 pennies 4 nickels, 16 pennies 3 nickels, 21 pennies 2 nickels, 26 pennies 1 nickel, 31 pennies 36 pennies
The combined height of 3 nickels is 0.24 inches, 2 nickels is 0.16 inches, and 1 nickel is 0.08 inches. Therefore, the combined height of 3 nickels, 2 nickels, and 1 nickel is 0.24 + 0.16 + 0.08 = 0.48 inches.
1 quarter, 1 dime, 1 penny 1 quarter, 2 nickels, 1 penny 1 quarter, 1 nickel, 6 pennies 3 dimes, 1 nickel, 1 penny 2 dimes, 3 nickels, 1 penny 2 dimes, 2 nickels, 6 pennies 2 dimes, 1 nickels, 11 pennies 1 dime, 4 nickels, 1 nickel, 1 penny 1 dime, 3 nickels, 11 pennies 1 dime, 2 nickels, 16 pennies 1 dime, 1 nickel, 21 pennies 7 nickels, 1 penny 6 nickels, 6 pennies 5 nickels, 11 pennies 4 nickels, 16 pennies 3 nickels, 21 pennies 2 nickels, 26 pennies 1 nickel, 31 pennies 36 pennies 1 Quarter, 11 pennies 1 Dime, and 26 Pennies And this makes 21 Ways
1 quarter-1 dime-1 nickel 1 quarter-1 dime-5 pennies 1 quarter-3 nickels 1 quarter 2 nickels-5 pennies 1 quarter-1 nickel-10 pennies 1 quarter-15 pennies 4 dimes 3 dimes-2 nickels 3 dimes-1 nickel-5 pennies 3 dimes- 10 pennies 2 dimes-4 nickels 2 dimes-3 nickels-5 pennies 2 dimes-2 nickels-10 pennies 2 dimes-1 nickel-15 pennies 2 dimes-20 pennies 1 dime-6 nickels 1 dime-5 nickels-5 pennies 1 dime-4 nickels- 10 pennies 1 dime-3 nickels-15 pennies 1 dime-2 nickels-20 pennies 1 dime-1 nickel-25 pennies 1 dime-30 pennies 8 nickels 7 nickels-5 pennies 6 nickels-10 pennies 5 nickels-15 pennies 4 nickels-20 pennies 3 nickels-25 pennies 2 nickels-30 pennies 1 nickel-35 pennies 40 pennies Total Number of Solutions=31
There are 12 different combinations using pennies, nickels and dimes. 25 pennies 20 pennies and 1 nickel 15 pennies and 2 nickels 15 pennies and 1 dime 10 pennies and 3 nickels 10 pennies 1 dime and 1 nickel 5 pennies and 4 nickels 5 pennies 1 dime and 2 nickels 5 pennies and 2 dimes 5 nickels 1 dime and 3 nickels 2 dimes and 1 nickel
50 pennies45 pennies, 1 nickel40 pennies, 2 nickels40 pennies, 1 dime35 pennies, 3 nickels35 pennies, 1 nickel, 1 dime30 pennies, 4 nickels30 pennies, 2 nickels, 1 dime30 pennies, 2 dimes25 pennies, 5 nickels25 pennies, 3 nickels, 1 dime25 pennies, 1 nickel, 2 dimes25 pennies, 1 quarter20 pennies, 6 nickels20 pennies, 4 nickels, 1 dime20 pennies, 2 nickels, 2 dimes20 pennies, 1 nickel, 1 quarter15 pennies, 7 nickels15 pennies, 5 nickels, 1 dime15 pennies, 3 nickels, 2 dimes15 pennies, 2 nickels, 1 quarter15 pennies, 1 nickel, 3 dimes10 pennies, 8 nickels10 pennies, 6 nickels, 1 dime10 pennies, 4 nickels, 2 dimes10 pennies, 3 nickels, 1 quarter10 pennies, 2 nickels, 3 dimes10 pennies, 1 nickel, 1 dime, 1 quarter10 pennies, 4 dimes5 pennies, 9 nickels5 pennies, 7 nickels, 1 dime5 pennies, 5 nickels, 2 dimes5 pennies, 4 nickels, 1 quarter5 pennies, 3 nickels, 3 dimes5 pennies, 2 nickels, 1 dime, 1 quarter5 pennies, 1 nickel, 4 dimes5 pennies, 2 dimes, 1 quarter10 nickels8 nickels, 1 dime6 nickels, 2 dimes5 nickels, 1 quarter4 nickels, 3 dimes3 nickels, 1 dime, 1 quarter2 nickels, 4 dimes1 nickel, 2 dimes, 1 quarter5 dimes2 quarters1 half dollar
Start with zero nickels, and see what the combinations are: There is only 1 combination, which is 3 dimes and 1 quarter.Next use only 1 nickel, then you have: 2 quarters & 1 nickel, or 5 dimes & 1 nickel, so that's 2 additional combinations.Keep going with only 3 nickels, etc, till you get to 11 nickels = 55 cents. Note that there is no way to do it with only 8 or 10 nickels.This is the groundwork for answering. The answer is not yet finished.
One quarter,or 25 pennies, or 20 pennies and 1 nickel, or 15 pennies and 2 nickels, or 10 pennies and 3 nickels or 5 pennies and 4 nickels, or 2 dimes and 1 nickel, or 1 dime and 3 nickels, or 15 nickels and 1 dime.
2 quarters 1 quarter, 2 dimes, 1 nickel 1 quarter, 1 dime, 3 nickels 1 quarter, 5 nickels 5 dimes 4 dimes, 2 nickels 3 dimes, 4 nickels 2 dimes, 6 nickels 1 dime, 8 nickels 10 nickels
12 combinations:One quarter2 dimes, 1 nickel2 dimes, 5 pennies1 dime, 3 nickels1 dime, 2 nickels, 5 pennies1 dime, 1 nickel, 10 pennies5 nickels4 nickels, 5 pennies3 nickels, 10 pennies2 nickels, 15 pennies1 nickel, 20 pennies25 pennies
20 pennies 1 nickel & 15 pennies 2 nickels & 10 pennies 3 nickels & 5 pennies 1 dime & 1 nickel & 5 pennies 2 dimes
I believe there are 13 ways 1 - 1(quarter) + 2(pennies) 2 - 2(dimes) + 1(nickel) + 2(pennies) 3 - 2(dimes) + 7(pennies) 4 - 1(dime) + 3(nickels) + 2(pennies) 5 - 1(dime) + 2(nickel) + 7(pennies) 6 - 1(dime) + 1(nickel) + 12(pennies) 7 - 1(dime) + 17(pennies) 8 - 5(nickels) + 2(pennies) 9 - 4(nickels) + 7(pennies) 10 - 3(nickels) + 12(pennies) 11 - 2(nickels) + 17(pennies) 12 - 1(nickel) + 22(pennies) 13 - 27(pennies)