Round 276

Date Released: August 28th, 2008.
Date Rewarded: September 4th, 2008.

The following sentence appears somewhere on the Neopets site. However, only one letter per word is shown here.

What Neopian name can you spell when you unscramble the circled letters? Only submit a single word as your answer; any other information may disqualify your entry.

Prize


Kougra Lily

Click to show/hide solution

It's funny that the above sentence is from Lenny Conundrum: "Also giving out the answer or obvious hints is against the rules."

That leave you with avtebhigrl to unscramble. The answer is brightvale.

Results: 5143 people guessed the correct answer earning themselves 389 NP each.

Round 275

Date Released: August 21st, 2008.
Date Rewarded: August 28th, 2008.

You have the following sequence of numbers:

24
___
___
9
___
15
19

If you multiply the three missing numbers together, what will you get?

Prize


Fresh Bamboo Mat

Click to show/hide solution

Check out the calendar.

* Aug 8th - Blumaroo Day
* Aug 11th - Discovery of Brightvale
* Aug 18th - Meerca Day!
* Aug 20th - Annual Usuki Doll Convention
* Aug 24th - Grundo Independence Day
* Aug 25th - Mutant Day
* Aug 29th - Kyrii Day

* Sept 9th - Draik Day
* Sept 13th - Techo Day
* Sept 15th - The Annual Chocolate Ball
* Sept 19th - Poogle Parade (Poogle Day)
* Sept 20th - Faerie Festival. Rumour has it that this is when the Faeries are most generous to Neopians.
* Sept 23rd - Annual Gormball Championships
* Sept 25th - Skeith Day

According to the original sequence, the missing numbers are 25, 29 and 13. Therefore, the answer is: 25 * 29 * 13 = 9425.

Results: 4405 people guessed the correct answer earning themselves 455 NP each.

Round 274

Date Released: August 14th, 2008.
Date Rewarded: August 21st, 2008.

A Chomby was walking down a path one day when Jhudora appeared in front of it. "Solve this puzzle, and you may pass," she said.

Suppose you have a bunch of wooden beds, each weighing 200 pounds each, arranged in a pyramid. The base layer is 5 beds by 5 beds, the layer above is 4 beds by 4 beds, and so on until the top layer of one bed. They are arranged in such a way that each bed is resting on four beds below it, one leg on each bed.

If the weight on each bed is always equally distributed to all four legs, and each bed leg can only support 200 pounds, how many pounds can you place on top of the topmost bed? Please round to the nearest pound, and plese submit only a single number as your answer.

Prize


Wooden Bed

Click to show/hide solution

If the weight on each bed is always equally distributed to all four legs, and each bed leg can only support 200 pounds => Each bed can support maximum 200 x 4 = 800 pounds.

Each bed weighs 200 pounds. Let x be the extra weight you can put on the top of the topmost bed. We will go from top to bottom level.

Top level: total weight = x + 200. Each bed leg can withstands: (x + 200) / 4.

2nd top level: see the below figure for visual help, the four red dots are the four legs of the top level bed. The total weight of each bed (including itself) = (x + 200) / 4 + 200 = (x + 1000) /4. Each bed leg withstands: (x + 1000) / 16.


3rd level: see the below figure for visual help, the red dots are the 2nd top level beds' legs.

* middle bed: the bed withstands 4 legs of the above 4 beds (one of each). Therefore, the total weight should be: (x + 1000) / 16 * 4 + 200 = (x + 1800) / 4. Each bed leg withstands: (x + 1800) / 16.

* side beds: each bed withstands 2 legs of the above 2 beds (one of each). Therefore, the total weight should be: (x + 1000) / 16 * 2 + 200 = (x + 2600) / 8. Each bed leg withstands: (x + 2600) / 32.

* corner beds: each bed withstands 1 leg of the above 1 bed. Therefore, the total weight should be: (x + 1000) / 16 + 200 = (x + 4200) / 16. Each bed leg withstands: (x + 4200) / 64.


4th level: see the below figure for visual help, the red dots are the 3rd level middle bed's legs, the yellow dots are the 3rd level side beds' legs and the blue red dots are the 3rd level corner beds' legs.

Since we only concern about the bed that withstand the most weights, we can ignore the side and corner beds and only consider the 4 middle beds which contributes most weights into the middle bed on the bottom level (see the bottom level figure). Each of the 4 middle beds withstand 1 leg from a 3rd level corner bed, 2 legs from 3rd level side beds, 1 leg from the 3rd level middle bed. Therefore, the total weight of each 4th level middle bed should be: (x + 1800) / 16 + (x + 2600) / 32 * 2 + (x + 4200) / 64 + 200 = (9x + 34600) / 64. Each bed leg withstands: (9x + 34600) / 256.


Bottom level: see the below figure for visual help, the red dots are the 4th level middle beds' legs, the yellow dots are the 4th level side beds' legs and the blue red dots are the 4th level corner beds' legs.

Similar to the 4th level, we only concern with the bed that has the most weight on. That bed is the middle bed. Therefore, the weight of on that bed is: (9x + 34600) / 256 * 4 + 200 = (9x + 47400) / 64. Each bed leg withstands: (9x + 47400) / 256.


We know that each beg leg can only withstand maximum 200 pounds. From all the levels, the bed that has most weights on is the middle bed of the bottom level. Therefore:

(9x + 47400) / 256 <= 200 <=> x <= 3800/9 = 422.22

Therefore, the answer is 422.

Results: 1432 people guessed the correct answer earning themselves 1397 NP each.

Round 273

Date Released: August 7th, 2008.
Date Rewarded: August 14th, 2008.

The following sentence appears somewhere on the Neopets site. However, only the vowels are shown here.

What Neopian name can you spell when you unscramble the circled letters? Only submit a single word as your answer; any other information may disqualify your entry.

Prize


Ten Dubloon Coin

Click to show/hide solution

If you check on Neopia Central, you see this "You can buy food or toys for your Neopet, collect rare items, magical potions, collectable cards, and even buy clothes!"

That leave you with cdlaabrse to unscramble. Since the prize is a Dubloon Coin, the Neopian character should be a pirate. It is Scarblade.

Results: 8507 people guessed the correct answer earning themselves 236 NP each.