## Dhaka Secondary 2011/1 (Higher Secondary 2011/1)

Problem for Secondary Group from Divisional Mathematical Olympiad will be solved here.
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BdMO
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### Dhaka Secondary 2011/1 (Higher Secondary 2011/1)

In a box there are \$50\$ gold rings of \$10\$ different sizes and \$75\$ silver rings of \$12\$ different sizes. The size of a gold ring might be the same as that of a silver ring. What is the minimum number of rings one need to pick up to be sure of having at least two rings different both in size and material?

Tahmid Hasan
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### Re: Dhaka Secondary 2011/1 (Higher Secondary 2011/1)

soln for num 1:
বড় ভালবাসি তোমায়,মা

*Mahi*
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### Re: Dhaka Secondary 2011/1 (Higher Secondary 2011/1)

The answer isn't the one Tahmid posted,it is as follows-

Use \$L^AT_EX\$, It makes our work a lot easier!

Zzzz
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### Re: Dhaka Secondary 2011/1 (Higher Secondary 2011/1)

*Mahi* wrote:The answer isn't the one Tahmid posted,it is as follows-
Worst scenario of picking 76 rings will be mmm... may be 50 silver rings and 26 gold rings which are of same size.
Every logical solution to a problem has its own beauty.

*Mahi*
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### Re: Dhaka Secondary 2011/1 (Higher Secondary 2011/1)

Zzzz wrote:
*Mahi* wrote:The answer isn't the one Tahmid posted,it is as follows-
Worst scenario of picking 76 rings will be mmm... may be 50 silver rings and 26 gold rings which are of same size.
It was the official solution as far as I know...........but I did exactly what tahmid did

Use \$L^AT_EX\$, It makes our work a lot easier!

Tahmid Hasan
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### Re: Dhaka Secondary 2011/1 (Higher Secondary 2011/1)

if anyone shows the answer is less than 106 then i'll put them in the set of 41 g coins and 64 s coins of the same size.so it's not possible.if anyone tries to disprove my ans then plz try to make the ans greater than
বড় ভালবাসি তোমায়,মা

Hasib
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### Re: Dhaka Secondary 2011/1 (Higher Secondary 2011/1)

i think the ans is 106
A man is not finished when he's defeated, he's finished when he quits.

Hasib
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### Re: Dhaka Secondary 2011/1 (Higher Secondary 2011/1)

if 76 coins picked, then the following things may b happened!

Let, pick all 75 silver ring, and pick 1 gold ring! :O may unfortunately 1 gold will be the same size with the silver ring! Slap me!!!!
A man is not finished when he's defeated, he's finished when he quits.

leonardo shawon
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### Re: Dhaka Secondary 2011/1 (Higher Secondary 2011/1)

i also agreed with Tahmid and Hasib. Size of gold rings might be the same size of silver rings.
Ibtehaz Shawon
BRAC University.

long way to go .....

sakib.creza
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### Re: Dhaka Secondary 2011/1 (Higher Secondary 2011/1)

What if among the 12 sizes of the silver ring 10 of them are same as the 10 sizes of the gold ring.so shudnt the size of the gold rings be a subset of the sizes of the silver rings. so with worst case scenario I think the answer shud be (50+73+1)=124. Please let me know if there is any bug in my answer.