Lenny Conundrum

Every week, The Neopets Team releases a new Lenny Conundrum puzzle, and each week that puzzle gets posted on our blog. You can discuss with others the answer in the comments and come up with a solution! We also discuss the Mystery Picture Answers aswell!

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Wednesday, December 19, 2012

Lenny Conundrum - Round #

A complete binary tree with a height of 5 has 31 nodes. How many nodes does a binary tree with a height of 97 have? Please do not round or use scientific notation.


Please submit the answer in numerical form WITHOUT commas.

Posted by LennyC Solver at 23:20

Comments (13)

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-3 Vote up Vote down
Vinson's avatar

Vinson · 642 weeks ago

2^5 - 1 = 31
2^97 - 1 =158456325028528675187087900672
+11 Vote up Vote down
Vinson's avatar

Vinson · 642 weeks ago

Oops, I meant

2^97 - 1 = 158456325028528675187087900671
3 replies · active 642 weeks ago
+2 Vote up Vote down
Cassiel's avatar

Cassiel · 642 weeks ago

Absolutely correct
0 Vote up Vote down
Dan's avatar

Dan · 642 weeks ago

how about Summation of 2^x from limit 0 to 96.
0 Vote up Vote down
McNegro's avatar

McNegro · 642 weeks ago

That's the same thing...
-2 Vote up Vote down
Amy's avatar

Amy · 642 weeks ago

97/5*31 = 601.4
0 Vote up Vote down
Sharon's avatar

Sharon · 642 weeks ago

my calculator wouldn't go that far into didgets so I ended up with 20 or so zeros...
But I think the formula for calculating the nodes is wrong, is the formula not n = (2^h +1 ) - 1 ??
When used that formula I couldn't get to 31 nodes when inserting height (h) = 5 so I used the one mentioned by Vinson..
+3 Vote up Vote down
SlightlyToasted's avatar

SlightlyToasted · 642 weeks ago

Whats the new Mystery Pic? Something Tyrannian, maybe?
-5 Vote up Vote down
MP 1171's avatar

MP 1171 · 642 weeks ago

Golden Khamette Stamp
http://www.facebook.com/neopestes
New page with answers!
0 Vote up Vote down
Nia's avatar

Nia · 642 weeks ago

158456325028528675187087900671 Is that the answer? ;/
-1 Vote up Vote down
spinnercat's avatar

spinnercat · 642 weeks ago

2^97-1 = 158456325028528675187087900671

Here's my code in JAVA that I used (since no calculator would have that precision), if anyone wants to check:

import java.math.BigInteger;
public class Neopets {
public static void main(String[] args){
BigInteger integer = new BigInteger("1");
for(int i=0;i<97;i++){
integer = integer.multiply(new BigInteger("2"));
}
System.out.println(integer.subtract(new BigInteger("1")));
}
}
1 reply · active 642 weeks ago
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Jiggyface's avatar

Jiggyface · 642 weeks ago

The calculator that came with windows can handle that. It's really not that big...
0 Vote up Vote down
Juli's avatar

Juli · 641 weeks ago

Please round to the nearest 10 and submit the answer in word form.

^

whats the answer in word form?

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