MathDB

p1. Due to the crisis, the salaries of the company's employees decreased by

1/5

. By what percentage should it be increased in order for it to reach its previous value?
p2. Can the sum of six different positive numbers equal their product?
p3. Points

A, B, C

and

B

are marked on the straight line. It is known that

AC = a

and

BP = b

. What is the distance between the midpoints of segments

AB

and

CB

? List all possibilities.
p4. Find the last three digits of

625^{19} + 376^{99}

.
p5. Citizens of five different countries sit at the round table (there may be several representatives from one country). It is known that for any two countries (out of the given five) there will be citizens of these countries sitting next to each other. What is the smallest number of people that can sit at the table?
p6. Can any rectangle be cut into

1999

pieces, from which you can form a square?
PS. You should use hide for answers. Collected [url=https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics]here.

Problem Statement