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

 Posts: 1007
 Joined: Sat Dec 09, 2017 1:32 pm
Re: BDMO 2019 : National : Junior : Pblm 05
BdMO National Junior 2019 P5
Answer:$2073$
By Using $PIE$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?
Answer:$2073$
 math_hunter
 Posts: 22
 Joined: Mon Sep 24, 2018 10:33 pm
 Contact:
Re: BDMO 2019 : National : Junior : Pblm 05
Please give the full solution. How it is possible using PIE?samiul_samin wrote: ↑Thu Mar 07, 2019 8:15 pmBdMO National Junior 2019 P5By Using $PIE$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?
Answer:$2073$

 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.
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
 Contact:
Re: BDMO 2019 : National : Junior : Pblm 05
How do I identify that the last removed number is 2025?samiul_samin wrote: ↑Sat Mar 09, 2019 10:05 amTake 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.

 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
 Contact:
Re: BDMO 2019 : National : Junior : Pblm 05
Where can I get a clear description about "PIE" and how to solve this problem using "PIE"?
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 doubleremoved 6th powers
Did I get the air of the solution?
(How do I tag you or other users?)
So I assume it's basically this: we first remove all squares and cubes, and then add up the doubleremoved 6th powers
Did I get the air of the solution?
(How do I tag you or other users?)

 Posts: 1007
 Joined: Sat Dec 09, 2017 1:32 pm
Re: BDMO 2019 : National : Junior : Pblm 05
Exactly this is the solution style.
Go to user control panel
Then, friends and foe
Search the member name &
Submit.
Here.math_hunter wrote: ↑Sun Mar 10, 2019 11:44 amWhere can I get a clear description about "PIE" and how to solve this problem using "PIE"?
 sakib17442
 Posts: 11
 Joined: Sun Apr 11, 2021 10:04 pm
 Contact:
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
Dr.Seuss