Answer to Question #307158 in Discrete Mathematics for Ash

Question

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)?

Answer 1

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 $6\times20=120$ coins.

Solution (b)

The possible number of rows will be

$2^6=64$

This can also be obtained, by

Therefore we need $6\times64=384$ coins

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