Sum of Ten
The sum of ten distinct positive integers is 100. What is the largest possible value of one of the numbers?
Age
11 to 14
Challenge level
Problem
The sum of ten distinct positive integers is 100.
What is the largest possible value of any of the ten integers?
This problem is taken from the UKMT Mathematical Challenges.
Student Solutions
Answer: 55
To make one number as large as possible, make the other 9 numbers as small as possible.
Other numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
This means the largest number can be 55.