## BDMO 2019 : National : Junior : Pblm 05

- math_hunter
**Posts:**22**Joined:**Mon Sep 24, 2018 10:33 pm-
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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:**1004**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-
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### 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:$2073$

- samiul_samin
**Posts:**1004**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$=2019+54=2073$.

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-
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### 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.

- samiul_samin
**Posts:**1004**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"?

### 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?)

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:**1004**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"?