Question

How many coins
When i dumped the change out of my pocket, I noticed that i could pay the exact price for any item from one cent up to and through one dollar without receiving any change. What is the fewest number of coins I could have had in my pocket if i had pennies, nickels, dimes, and quarters? What are the coins?

Answer 1

4 pennies
1 nickle
2 dimes
3 quarters

Answer 2

start with
4 pennies, 2 nickels , 2 dimes , 3 quarters

covers from
1 to 9 --- 1 nickel, 4 pennies
10 to 14 -- 1 dime, 4 pennies
15 to 19 = 1 dime, 1 nickel, 4 pennies
20 to 24 = 1 dime, 2 nickels 4 pennies OR 2 dimes 4 pennies
25 to 29 --- 1 quarter, 4 pennies
30 to 34 --- 1 quarter, 1 nickel, 4 pennies
35 to 39 ---- 1 quarter, 1 dime, 4 pennies
40 to 44 ---- 1 quarter, 1 nickel, 1 dime, 4 pennies
45-49 -------1 quarter, 2 nickels 1 dime, 4 pennies
50 - 54 ---- 1 quarter, 2 dimes, 1 nickel, 4 pennies
55 - 59 --- 2 quarters, 1 nickel, 4 pennies
60 - 64 ---- 2 quarters, 1 dime, 3 pennies
65 - 69 --- 2 quarters , 1 dime, 1 nickel, 4 pennies
70-74 --- 2 quarters, 2 dimes, 4 pennies
75 -79 -- 2 quarters, 2 dimes, 1 nickel, 4 pennies
80 - 84 --- 2 quarters, 2 dimes, 1 nickel, 4 pennies OR 3 quarters, 1 nickel, 4 pennies
85-89 --- 3 quarters, 1 dime, 4 pennies
90-94 --- 3 quarters, 1 dime, 1 nickel, 4 pennies
95 -99 --- 3 quarters , 2 dimes, 4 pennies
100 ------ 3 quarters, 2 dimes, 1 nickel

to do 95 - 99 with only 2 quarters would need
2 quarters, 4 dimes, 1 nickel, 4 pennies

so I could cover any amount from 1 to 100 with

a) 4 pennies, 2 nickels, 2 dimes, and 3 quarters. for a total of 11 coins
or
b) 4 pennies, 2 nickels, 4 dimes, and 2 quarters for a total of 12 coins

Therefore:
4 pennies
2 nickels
2 dimes
3 quarters or a total of 11 coins

Answer 3

ARRGGGHHHH!!!!

looks like I messed up in my 45-49
could be done with 1 quarter, 2 dimes, and 4 pennies.
Nowhere else do we actually need 2 nickels

so as bobpursley said
3 quarters,
2 dimes
1 nickel
4 pennies for a total of 10 coins