Question

if x1,x2,...x10 is 100 and xi + xi+1 = 100 ,if x10= 1 find x1 ​

Answer 1

Answer:

Determine the number of solutions of the equation i+r+.+1 100 in positive integers not exceeding 30. Directions: First find how many solutions this equation has if all ri's are positive integers and there are no other constraints. Then find how many solutions this equation has if all ri's are positive integers and one of them, say x1, is constrained to be > 30. To do this, ,rio More generally, for a subset S of 1,2,. ,10) find how 30 for consider xi-30, x2, x3, consider T1 many solutions the equation has if al xi's are positive integers and, in addition, z, all j E S. Apply the Inclusion-Exclusion Principle. Notice what happens if ISI 2 4.

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