A list of 10 positive integers, each less than 15, has an average of 6. What is the maximum number of ones (the number 1, not the digit) that could be in the list?
+128474 Here's my best shot
If the 10 ntegers have an average of 6.....then the total sum of the integers must be 10 * 6 = 60 because 60 / 10 = 6
Therefore......we want to make the sum of the "non-one" digits as small as possible and the number of ones as large as possible
Possible Number of 1's Sum of the other digits
1 59
2 58
3 57
4 56
5 55
6 54
7 53
8 52
9 51
10 50
The last is clealrly not possible ( all ones)
The next-to-the last is also not possible......the largest sum that could be created with 9 ones is 9 + 14 = 23
The third-to-the last is also not possible ...the largest possible sum = 8 ones + 2 * 14 = 36
The fourth-to-the-last is also not possible....the largest sum = 7 ones + 3 * 14 = 49
Six ones is possible because 14 + 14 + 13 + 13 = 54
So....the max number of 1s = 6
