BdMO National Primary 2016 Problemset

samiul_samin
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BdMO National Primary 2016 Problemset

Problem 1.
If a $1$ mile long train crosses a $2$ mile platform in $1$ minute,then what is the required time for $2016$ mile long train of same speed while crossing a $2016$ mile platform?

Problem 2
$(11+11) \times(12+12)\times (13+13)...\times(18+18)\times(19+19)=x$

What is the remainder ,if $x$ is divided by $10$?

Problem 3
The sum of the digits of some two digits number is $11$ and these number can be written as the product of only two prime numbers.What is the sum of these two digits numbers?

Problem 4
Jannat had some marbles and she gave half of these to Mahi.Then she divided rest of the marble in two groups so that one group had one more marble than the other group.She gave half of the marbles of the group that contains even number of marbles to Tasnina.Finally she had four marbles remaining.How many marbles she had at first?

Problem 5
There are $7$ violet balls, $6$ blue balls, $5$ ndigo balls, $4$ green balls, $3$ yellow balls, $2$ orange balls and $1$ red ball. They should be kept at minimum number of boxes in such a way that no box contains more than one ball of same color and each box contains same number of balls. What is the number of balls in each box?

Problem 6
A number is called Tamata Number if it stays the same when the number is written in reverse order.For example, $121$ is a Tamata Number because,we get $121$, if $121$ is written in reverse order.Now what is the minimum G.C.D. (Greatest Common Divisor) of two four digit Tamata Number?

Problem 7

The floor of a museum is shaped like a simple polygon where the sides of the polygon have no points of intrsection except the adjacent sides.The walls of the museum are along the sides of the polygon.Guards have to be employed to guard the valuable things in the museum.Every guard can cover up the infinity around him but if there is a wall,he cannot watch beyond the wall.If the number of sides of the polygon is $n$,then prove that it is possible to guard the museum completely with minimum $\lfloor x/3\rfloor$ .[ $\lfloor x\rfloor$ is the biggest integer which is not bigger then $x$]?