MathDB

Several distinct real numbers are written on a blackboard. Peter wants to make an expression such that its values are exactly these numbers. To make such an expression, he may use any real numbers, brackets, and usual signs

+

-

and

\times

. He may also use a special sign

\pm

: computing the values of the resulting expression, he chooses values

+

-

for every

\pm

in all possible combinations. For instance, the expression

5 \pm 1

results in

\{4, 6 \}

, and

(2 \pm 0.5) \pm 0.5

results in

\{1, 2, 3 \}

. Can Pete construct such an expression:

a)

If the numbers on the blackboard are

1, 2, 4

;

b)

For any collection of

100

distinct real numbers on a blackboard?

Problem Statement