*BdMO*math campers were painted by

*Urmi*. Exactly $k$ colors were used in each picture. There is a common color in every $20$ pictures. But, there is no common color in all $100$ pictures. Find the smallest possible value of $k.$

- Kazi_Zareer
**Posts:**86**Joined:**Thu Aug 20, 2015 7:11 pm**Location:**Malibagh,Dhaka-1217

$100$ pictures of * BdMO* math campers were painted by *Urmi*. Exactly $k$ colors were used in each picture. There is a common color in every $20$ pictures. But, there is no common color in all $100$ pictures. Find the smallest possible value of $k.$

We cannot solve our problems with the same thinking we used when we create them.

$Exactly$ $one$ or $at$ $least$ $one$?

- samiul_samin
**Posts:**1004**Joined:**Sat Dec 09, 2017 1:32 pm

If I can show an example by setting $k=2$then the lowest value of $k$ is 2.But,is it enogh to show just one example to get the full solution?

$K$ may not be $2$

- samiul_samin
**Posts:**1004**Joined:**Sat Dec 09, 2017 1:32 pm

I am posting my solution.It may be wrong.

My confusion is here. Does it mean

If the first case is true, your solution is wrong. Because in $80$ pictures, you will get $2$

If the second case is true, this solution is just like mine!

- samiul_samin
**Posts:**1004**Joined:**Sat Dec 09, 2017 1:32 pm

What is the solution if the first case is true?Tasnood wrote: ↑Tue Feb 20, 2018 8:08 amMy confusion is here. Does it meanjust one common color in every 20 picturesorat least one among 20?

If the first case is true, your solution is wrong. Because in $80$ pictures, you will get $2$(B,G)common color. The answer should be $9$

If the second case is true, this solution is just like mine!

[As a problem $7 of secondary level, it might not be very easy.

If the first case is true, you can't use two colors in $20$ pictures. The answer should be $9$

I think the condition is for ,any 20 pics share a common colour, but not all of them share the same colour.

If that so ,then the answer is 3.

If that so ,then the answer is 3.

- samiul_samin
**Posts:**1004**Joined:**Sat Dec 09, 2017 1:32 pm