**Bangladesh National Mathematical Olympiad 2014:**

Primary

Primary

Problem 1

If a number is multiplied by itself then the obtained product is a square number.For example,$2\times2=4$ is a square number.The sum of three consequative positive integers is a square number.Which is the smallest such square number?

Problem 2

When, $x$ is divided by $10$, the quotient is $y$,with a remainder of $4$. If $x$ and $y$ are both positive integers,what is the remainder when $x$ is divided by $5?$

Problem 3

Rubai and Bidushi have some marbles.Bidushi told Rubai ,"if you give me some marbles,I will return one more marble tuan as many as you gave me. "Rubai said,"Alright I will first give you $6 $ marbles.Then Rubai gave Bidushi $6$ marbles and Bidushi returned $7$ marbles to Rubai.Thus after they have exchanged marble $5$ times,Bidushi had no marbles left.How many marbles Bidushi have in the beginning?

Problem 4

Subrata has invented a new type of clock,according to which, there are $15$ hours in each day and $80$ minutes in each hour. For example Subrata's clock shows $10:00$ when the actual time is $16:00$ in a traditional clock. If the time is $20:36$ in a traditional clock, then what will be the time in Subrata's clock ?

Problem 5

How many four digits numbers are there for which ,the number formed by its last two digits in the same order when multiplied by three gives us the number formed by its first two digits in the same order?For example, $3612$ is such a number where the number formed by the last two digits in the same order is $12$ and when multiplied by $3$ gives $36$.

Problem 6

.A work has to be done in $18$days.A contructor assigned $20$ men to do the tusk.But,after $10$ days it was found that only half of the work was done.So,how many men should he add so that the work will be finshed in time?

Problem 7

A new series is to be formed by removing some terms from the series $1,2,3,4,.........,30$

such that no terms of the new series is obtained if the new series is doubled.Maximum how many terms can be in the new series?

Problem 8

Is it possible to completely cover a $14*14$ grid by "T" shaped blocks from the diagram such that no block overlaps any other bolcks? Explain your answer with logic.