Question #307158

You break your piggy-bank to discover lots of pennies and nickels. You start arranging these in rows of 6 coins. Show all your steps with written explanation.



(a) You find yourself making rows containing an equal number of


pennies and nickels. For fun, you decide to lay out every possible


such row. How many coins will you need?



b) How many coins would you need to make all possible rows


of 6 coins (not necessarily with equal number of pennies and


nickels)?

1
Expert's answer
2022-03-07T22:32:01-0500

Solution (a)


Here, each row is a 6-bit string (6 coins)

Its weight is 3 (3 pennies)


Therefore, the possible number of rows will be




And in case each row requires 6 coins simultaneously, we need 6×20=1206\times20=120 coins.


Solution (b)


The possible number of rows will be


26=642^6=64


This can also be obtained, by




Therefore we need 6×64=3846\times64=384 coins


3842=192\frac{384}{2}=192 coins in each row.





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