Questions 1 to 10 are worth 3 points, 11 to 20 are worth 4 points and 21 to 25 are worth 5 points. Questions 26 to 30 are worth 6, 7, 8, 9 and 10 points, respectively.

No penalties apply for wrong attempts. Maximum score equals 135 points.

The first 25 questions are multiple choice with 5 choices. The last 5 questions have an integer answer between 0 and 999.

Here are sample questions used recently in the last 5 questions, which are typical of those with 0–999 integer solutions.

### SAMPLE QUESTIONS

#### Junior

The sum of the digits of the number 2004 is 6. How many whole numbers from 1000 to 9999 have 6 as the sum of their digits?

#### Intermediate

The Fibonacci numbers are *F*(1)=1, *F*(2)=1, *F*(3)=2, *F*(4)=3, *F*(5)=5, *F*(6)=8, *F*(7)=13, … where the first two are both equal to 1, and from then on, each one is the sum of the two preceding it. Of the first 2004 Fibonacci numbers, how many have 2 as their last digit?

#### Senior

Seven numbers, each 1 or -1, are listed in a row in such a way that adding the numbers successively from left to right never gives a negative answer. For example, 1 -1 1 1 -1 -1 1 has successive sums 1, 0, 1, 2, 1, 0, 1 and is valid, while 1 1 -1 -1 -1 1 1 has successive sums 1, 2, 1, 0, -1, 0, 1, and is not valid. How many valid lists are there?

### THE MARK SENSE SHEET

The mark sense sheet is double sided. Below we show the reverse side, which is used to answer the questions.