MathDB

A magician has

300

cards with numbers from

1

300

written on them, each number on exactly one card. The magician then lays these cards on a

3 \times 100

rectangle in the following way - one card in each unit square so that the number cannot be seen and cards with consecutive numbers are in neighbouring squares. Afterwards, the magician turns over

k

cards of his choice. What is the smallest value of

k

for which it can happen that the opened cards definitely determine the exact positions of all other cards?

Problem Statement