MathDB

Let

X

denotes the set of integers from

1

239

. A magician with an assistant perform a trick. The magician leaves the hall and the spectator writes a sequence of

10

elements on the board from the set

X

. The magician’s assistant looks at them and adds

k

more elements from

X

to the existing sequence. After that the spectator replaces three of these

k+10

numbers by random elements of

X

(it is permitted to change them by themselves, that is to not change anything at all, for example). The magician enters and looks at the resulting row of

k+10

numbers and without error names the original

10

numbers written by the spectator. Find the minimal possible

k

for which the trick is possible.

Problem Statement