5th and 6th graders

February 2015


B.1009. 
Steve's rectangular shaped window is divided into 3x3 smaller sections. Steve paints a few of those sections yellow so that the whole window looks just the same from the outside than from the inside. How many different ways can he do this if he paints yellow
a) 2 sections

b) 3 sections?
B.1010. Find the 2015th digit to the right of the decimal point in the expansion of 1/13.

B.1011. A person is considered to be lucky if his/her 8-digit birth date is a palindrome number. (A number is a palindrome if it is the same when read backwards.) In the 8-digit birth date the first 4 digits are for the year, the next two digits are for the month and the last 2 digits are for the day. (The day and the month are always written by 2-digit numbers.) How many such birth dates are there in the spring months of the year between the years 1000 and 2015? When is the next such birth date?

B.1012. It takes a bus 30 minutes to go from A to B. There is a bus leaving every 2 minutes from A. At the same time with a bus, a car leaves from A. It takes the car 7.5 minutes to get to B. How many buses did the car pass on its way to B (not including the bus it started with)?

B.1013. What are the last two digits of the 2015th power of 7?

B.1014. You have three number cards. Each card has a digit on it that is different from the other two digits. Using these cards, create all possible 1-, 2-, and 3-digit numbers. The sum of these numbers is 5635. What are the digits on the cards?

B.1015. Ann, Beatrix, Cecilia, Diana, and Emma are going to the movies where they want to sit in 5 consecutive seats. However, Ann wants to sit next to Beatrix, and Diana wants to sit next to Emma, but Cecilia does not want to sit next to Emma. How many different ways can the girls sit down?

B.1016. In a faraway country there are only 3-, 5-, and 7-rupee coins. How many different ways can you pay 40 rupees if you are not allowed to get any money back?

Please, send your solutions here.


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