**B. 4056.** The orthocentre of an acute-angled triangle is *M*, the centre of its circumscribed circle is *O*, and its sides are *a*<*b*<*c*. The line of side *c*, the line of the altitude drawn to side *b*, and the line *MO* form a triangle that is similar to the original triangle but with opposite orientation. Find the angles of the triangle.

Suggested by *J. Bodnár,* Budapest

(4 points)

**K. 153.** Steve has a four-digit number in mind that Alex has to guess. Alex chooses a four-digit number, and Steve tells him how many digits it contains that stand in the appropriate position. [For example, if the number to find out is 1234 and the guess is 6231, then 2 digits are correct: 2 and 3. (The 1 does not count, since that is not in the right position.)] Alex had nine guesses: 2186, 5127, 6924, 4351, 5916, 8253, 4521, 6384, 8517. In each of the nine numbers, he guessed exactly one digit right, that is, each of the nine numbers contains exactly one digit that stands in the right position. What is the number that Steve has in mind?

(6 points)

This problem is for grade 9 students only.