# HUES 6th Grade Math Choice #4 25-Jan-2000

Hollis Upper Elementary School, Hollis, New Hampshire

1. 1992-1993 6th grade math contest

Source: The Math League
http://www.mathleague.com

2. RUNSUMS

A run of numbers is a collection of whole numbers with no gaps in it, such as 2, 3, 4; but not 5, 6, 8, 9 because 7 is missing.  2, 3, 3 is not a run because 3 is repeated.  Practically  all numbers can be written as a sum of a run (we will not allow a run to start at 0).  For example, 9 = 2 + 3 + 4, 10 = 1 + 2 + 3 + 4, 11 = 5 + 6 and we will can them RUNSUMS.  Note that there is no RUNSUM of 4 or 8.

2A. What is the smallest number that is a sum of a run of 3 numbers?
2B. What is the smallest number that is a sum of a run of 4 numbers?
2C. What is the smallest number that is a sum of a run of 5 numbers?
2D. What is the smallest number that is a sum of a run of 10 numbers?
2E. What is the smallest number that is a sum of a run of 100 numbers?
2F. What is the smallest number that is a sum of a run of 'n' numbers?

Source: The Math Forum
http://forum.swarthmore.edu/midpow/solutions/solution.ehtml?puzzle=18

Don Braffitt