401

Part of 1985 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 401 All Soviet Union MO 1985 like pascal triangle, min wanted

Source:

In the diagram below

a, b, c, d, e, f, g, h, i, j

are distinct positive integers and each (except

a, e, h

j

) is the sum of the two numbers to the left and above. For example,

b = a + e, f = e + h, i = h + j

. What is the smallest possible value of

d

?
j h i e f g a b c d

Pascal's Triangletriangle tablecombinatoricsminimumSum