This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

1985 All Soviet Union Mathematical Olympiad, 401
In the diagram below $a, b, c, d, e, f, g, h, i, j$ are distinct positive integers and each (except $a, e, h$ and $j$) 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
minimum pascal triangle combinatorics sum triangle table number theory

1972 All Soviet Union Mathematical Olympiad, 163
The triangle table is constructed according to the rule: You put the natural number $a>1$ in the upper row, and then you write under the number $k$ from the left side $k^2$, and from the right side -- $(k+1)$. For example, if $a = 2$, you get the table on the picture. Prove that all the numbers on each particular line are different. 2 / \ / \ 4 3 / \ / \ 16 5 9 4 / \ / \ /\ / \
combinatorics algebra triangle table geometry