## BDMO 2019 : National : Junior : Pblm 05

For students of class 6-8 (age 12 to 14)
math_hunter
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### BDMO 2019 : National : Junior : Pblm 05

2,3,5,6,7,10,11,12,13,... is the sequence of integers without all square and cube numbers. What is the 2019th number?

samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### Re: BDMO 2019 : National : Junior : Pblm 05

BdMO National Junior 2019 P5
math_hunter wrote:
Thu Mar 07, 2019 11:52 am
$2,3,5,6,7,10,11,12,13,...$ is the sequence of integers without all square and cube numbers. What is the $2019^{th}$ number?
By Using $PIE$
Answer:$2073$

math_hunter
Posts: 22
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### Re: BDMO 2019 : National : Junior : Pblm 05

samiul_samin wrote:
Thu Mar 07, 2019 8:15 pm
BdMO National Junior 2019 P5
math_hunter wrote:
Thu Mar 07, 2019 11:52 am
$2,3,5,6,7,10,11,12,13,...$ is the sequence of integers without all square and cube numbers. What is the $2019^{th}$ number?
By Using $PIE$
Answer:$2073$
Please give the full solution. How it is possible using PIE?

samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### Re: BDMO 2019 : National : Junior : Pblm 05

Take squares and cubes,
Remove the $6^{th}$ powers,
Giving us $54$ numbers to remove.Last removed number is $2025$
Thus we get our $2019^{th}$ number$=2019+54=2073$.

PIE=Inclusion Exclusion Principle

Try for smaller cases(70 or 100) to understand the solution clearly.

math_hunter
Posts: 22
Joined: Mon Sep 24, 2018 10:33 pm
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### Re: BDMO 2019 : National : Junior : Pblm 05

samiul_samin wrote:
Sat Mar 09, 2019 10:05 am
Take squares and cubes,
Remove the $6^{th}$ powers,
Giving us $54$ numbers to remove.Last removed number is $2025$
Thus we get our $2019^{th}$ number$=2019+54=2073$.

PIE=Inclusion Exclusion Principle

Try for smaller cases(70 or 100) to understand the solution clearly.
How do I identify that the last removed number is 2025?

samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### Re: BDMO 2019 : National : Junior : Pblm 05

Try for smaller cases and write down the squares and cubes from $2000$ to $2100$.You will understand.I am sorry that my solution is not clear enough to understand.

math_hunter
Posts: 22
Joined: Mon Sep 24, 2018 10:33 pm
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### Re: BDMO 2019 : National : Junior : Pblm 05

Where can I get a clear description about "PIE" and how to solve this problem using "PIE"?

vyper47
Posts: 4
Joined: Fri Mar 30, 2018 4:56 pm

### Re: BDMO 2019 : National : Junior : Pblm 05

samiul_samin

So I assume it's basically this: we first remove all squares and cubes, and then add up the double-removed 6th powers

Did I get the air of the solution?

(How do I tag you or other users?)

samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### Re: BDMO 2019 : National : Junior : Pblm 05

vyper47 wrote:
Sun Mar 10, 2019 12:55 pm
samiul_samin

So I assume it's basically this: we first remove all squares and cubes, and then add up the double-removed 6th powers

Did I get the air of the solution?
Exactly this is the solution style.
vyper47 wrote:
Sun Mar 10, 2019 12:55 pm
@samiul_samin
(How do I tag you or other users?)
Go to user control panel
Then, friends and foe
Search the member name &
Submit.
math_hunter wrote:
Sun Mar 10, 2019 11:44 am
Where can I get a clear description about "PIE" and how to solve this problem using "PIE"?
Here.

sakib17442
Posts: 11
Joined: Sun Apr 11, 2021 10:04 pm
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### Re: BDMO 2019 : National : Junior : Pblm 05

Well, samiul_samin's solution is perfectly correct. But for better understanding, I am elaborating this a bit. Okay, here is the full solution:
Games You can't win because you'll play against yourself.
---Dr.Seuss