Bangladesh National Mathematical Olympiad 2013: Primary

Problem $1$:

A group of $7$ women takes $7$ days to make $7$ Nokshikatha. How many days will a group of $5$ women take for making $5$ Nokshikatha?

http://www.matholympiad.org.bd/forum/vi ... =13&t=2905

Problem $2$:

Nazia's mobile phone has a strange problem. Each time she sends an SMS, it is also sent to all the existing numbers of her call list. The actual recipient of the SMS is then added to her call list.. At some point, Nazia deleted her call list. The next SMS she sent was the $16^{th}$ SMS sent from her mobile phone. How many numbers were there in her call list before she deleted her call list?

http://www.matholympiad.org.bd/forum/vi ... =13&t=2906

Problem $3$:

A cube-shaped room has six walls (floor, roof and east, west, north, south walls). A grasshopper is sitting at the south-west corner of the floor. The grasshopper needs to go to the north-east corner of the roof by jumping upward, northward or eastward and in each jump it goes one-third of the room's length. If the grasshopper gets $5$ points for each upward jump, $3$ points for each eastward jump and $1$ point for each northward jump, then what is the difference of the maximum and the minimum number of points it can have when it reaches its destination?

http://www.matholympiad.org.bd/forum/vi ... =13&t=2907

Problem $4$:

The English alphabets are arranged in $3$ rows in a Keyboard. Now somebody presses one key in the first row in such a way that there are same number of keys on both sides of that key in that row. Now a second person presses a key in the second row in the same way and a third person also does the same in the third row. Show that it is impossible.

http://www.matholympiad.org.bd/forum/vi ... =13&t=2908

Problem $5$:

For any two numbers $x$ and $y$, the absolute value of $x$ and $y$ is defined as $|x-y| = $ difference between the numbers $x$ and $y$. For example, $|5-2| = 3, |3-9| = 6$. Let $a_1, a_2, a_3, ... ... ..., a_n$ be a sequence of numbers such that each term in the sequence is larger than the previous term.

Let $S = |a_1 - a_2| + |a_2 - a_3|+ … + |a_{n-1} - a_n|$. What is the minimum number of numbers that you need to know from the sequence in order to find $S$?

http://www.matholympiad.org.bd/forum/vi ... =13&t=2909

Problem $6$:

A polygon is an area bounded by three or more edges in a plane. For example a triangle has three edges, a quadrilateral has four edges, a pentagon has five edges and in this way they are given names according to their number of edges. A regular polygon is a polygon that has edges of equal lengths and all of it's angles are equal as well.

Your father is going to set tiles on your room’s floor. He asked your choice of tiles(polygon). But there are some conditions.

(a) You can choose only one type of regular polygon.

(b) When tiles will be set, there must be no gap among them.

(c) No overlapping is allowed.

(d) You should not be concerned about your room size, rather the above three conditions.

Which type of the regular polygon can you use to draw such a figure that satisfies the above conditions? Write down the logic of not using other regular polygons rather than the one/s you chose. Here is a sample picture for you.

http://www.matholympiad.org.bd/forum/vi ... =13&t=2910

Problem $7$:

Arefin, Farhad, Himu, Mahdi, Rachi, Sadia and Tusher are seven friends who live in Gulshan by the side of same linear road. Distances of others home from Tusher home are given below. Tusher’s home is at the starting point of that road. They want to meet at the same place on that road every evening for gossiping. Find a place on that road so that the sum of distances of that place from everyone’s home is minimum. Write down your logic and distance of that place from Tusher’s home.

http://www.matholympiad.org.bd/forum/vi ... =13&t=2911

Problem $8$:

There are some boys and girls in a class. Every boy is friends with exactly three girls, and every girl is friends with exactly three boys. If there are $13$ boys in the class, how many girls are there? (Assume that friendship is mutual, i.e. if $A$ is friend of $B$ then $B$ is also friend of $A$.)

http://www.matholympiad.org.bd/forum/vi ... =13&t=2912