Question 946695
You may need to assume one of the counts of coins to be an unknown constant.


p,n,d,q the count of each coin.


{{{system(p+n+d+q=14,0.01p+0.05n+0.10d+0.25q=1.56)}}}



{{{system(p+n+d+q=14,p+5n+10d+25q=156)}}}


Maybe easier to start with dimes and or nickels and work from those splitting and combining to adjust to 14 coins.  Fourteen dimes would be a few cents short...


Another direction is to start with the most efficient coin combination and adjust to use more coins from there.
Begin with 6 quarters, 1 nickel, 1 penny.
Convert one of the quarters to all nickels; how many coins?
continue trying to find further adjustments...