1. There are four buttons in a row, as shown below. Two of them show happy faces, and two of them show sad faces. If we press on a face, its expression turns to the opposite (e.g. a happy face turns into a sad face). In addition, the adjacent buttons also change their expressions. What is the least number of times you need to press a button in order to turn them all into happy faces?

2. Place the numbers 1 to 9 in the empty white boxes so that the 3 horizontal and 3 vertical equations are true. Each digit can be used exactly once. Calculations are done from left to right and from top to bottom.

3. ABCD is a quadrilateral ∠BAD = ∠CED = 90◦∠ABC = 135, AB = 18cm, CE = 15cm, DE = 36cm. Find the area of the quadrilateral ABCD.

4. Starting from the far left circle, move along the lines to the far right circle, collect the numbers in the circles, the diamonds, and the ovals as you go (each can be picked only once). The ovals equal −10 and the diamonds equal −15, respectively. What are the minimum and maximum total sums you can gain?

5. Each number from one to nine appears twice on the eighteen disks that are hanging by threads. Your task is to cut the least number of threads to leave only nine disks hanging that have each number from one to nine. Find the least number of threads you need to cut.

7. Two smart students A and B participate in a mental quiz bowl. The Quizmaster reads the question, "Guess a two-digit number that can be divided by 7. I have two cube cards, each with a number printed on them. The number on the first card represents the sum of the digits of this number, while the product of the number's two digits is printed on the second card. Each of you will pick one card and do the analysis on your own". After reading the card, each of them says that they cannot predict what the two-digit number is, but right after listening to each other's statement, they immediately say, "I know", and they both give the correct answer. What is the number?

8. On Saturday, Jimmy started painting his toy helicopter between 9:00 am and 10:00 am. When he finished between 10:00 and 11:00 am on the same morning, he found the hour and minute hands exactly switched places: the hour hand was exactly where the minute hand had been, and the minute hand was exactly where the hour hand had been when he started. Jimmy spent hours painting. Determine the value of t.

9. Hoa likes to build models of three-dimensional objects from square ruled paper. Last time she used scissors to cut out a shape as shown in the figure below. Then she glued it together in such a way that no two squares were overlapping, there was no holes on the surface of the resultant object and it had nonzero volume. How many vertices did this object have? Note, that by a vertex we mean a vertex of the three-dimensional object, not a lattice point on the paper.

10. 32 teams are competing in a basketball tournament. At each stage, the teams are divided into groups of 4. In each group, every team plays exactly once against every other team. The best two teams are qualified for the next round, while the other two are eliminated. After the last stage, the two remaining teams play one final match to determine the winner. How many matches will be played in the whole tournament?