Monday

December 22, 2014

December 22, 2014

Posted by **DAVID** on Thursday, April 15, 2010 at 3:52am.

in the set whose sum is also in the set. [Repetitions are allowed.]

For example, the set U = {2, 3, 7} has TSP since 2 + 2 + 3 = 7, while V = {2, 3, 10} fails to have TSP.

(a) Suppose the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} is separated into two parts,

forming two subsets A and B.

Prove: Either A or B must have the triple-sum property.

[To begin the proof, suppose that statement is false and there are sets A and B as above, each without TSP.

If 1 lies in A then 3 = 1 + 1 + 1 must be in B. Complete the proof that this situation is impossible.]

(b) Is a similar result true when the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is separated into two parts?

**Answer this Question**

**Related Questions**

math - Sum of 8numbers is X,sum of a different set of nine numbers is 2x.average...

math - Can anyone explain please,thank.the sum of 8numbers is x,and the sum of ...

Math riddle - nine odd numbers have a sum of 243.find the sum of the first and ...

Math riddle - nine odd numbers have a sum of 243.find the sum of the first and ...

Math - The average of a set of 7consecutivr positive intergers is 15. What is ...

Integers - Suppose a1, a2, . . . , an is a list of n numbers with the following ...

math URGENT!!!! - i have a list of 5 different numbers. the sum of 2 of the ...

6TH GR. ALGEBRA - EXTENDING THE LESSON If you add any two rational numbers, the...

math - The set S has the property that if a is in S, then a squared + a is also ...

SAT prep help - Set M consists of the consecutive integers from -15 to y, ...