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Found: 3

Problem #PRU-35282

Problems Algebra and arithmetic Algebraic equations and systems of equations

12–14

Solve the equation \(xy = x + y\) in integers.

Problem #PRU-65263

Problems Probability and statistics Probability theory Discrete distribution Algebra and arithmetic Algebraic inequalities and systems of inequalities Quadratic inequalites (several variables) Algebraic equations and systems of equations Systems of algebraic non-linear equations

13–16 4.0

Is it possible to:

a) load two coins so that the probability of “heads” and “tails” were different, and the probability of getting any of the combinations “tails, tails,” “heads, tails”, “heads, heads” be the same?

b) load two dice so that the probability of getting any amount from 2 to 12 would be the same?

Problem #PRU-78244

Problems Algebra and arithmetic Absolute value Absolute value of a number (other) Number systems Decimal number system Algebraic equations and systems of equations Higher order equations. Palindromic polynomial equations Equations of higher order (other)

11–13 4.0

Two people play a game with the following rules: one of them guesses a set of integers \((x_1, x_2, \dots , x_n)\) which are single-valued digits and can be either positive or negative. The second person is allowed to ask what is the sum \(a_1x_1 + \dots + a_nx_n\), where \((a_1, \dots ,a_n)\) is any set. What is the smallest number of questions for which the guesser recognizes the intended set?