MathDB

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Part of 2022 Czech-Polish-Slovak Junior Match

Problems(2)

min different values of sums of 2 reals out of n

Source: 2022 Czech-Polish-Slovak Match Junior, individual p1 CPSJ

9/3/2022
Let n≥3n\ge 3. Suppose a1,a2,...,ana_1, a_2, ... , a_n are nn distinct in pairs real numbers. In terms of nn, find the smallest possible number of different assumed values by the following nn numbers: a1+a2,a2+a3,...,an−1+an,an+a1a_1 + a_2, a_2 + a_3,..., a_{n- 1} + a_n, a_n + a_1
combinatoricsalgebra
max of ab+bc+ 2ac for a,b,c>=0 with a+b+c=1

Source: 2022 Czech-Polish-Slovak Match Junior, team p1 CPSJ

9/3/2022
Determine the largest possible value of the expression ab+bc+2acab+bc+ 2ac for non-negative real numbers a,b,ca, b, c whose sum is 11.
algebrainequalities