## Wednesday, December 31, 2008

### Round 292

## Wednesday, December 17, 2008

### Round 291

http://www.neopets.com/faerieland/hiddentower938.phtml

Use the second letter of each item to get the question and check the Hidden Tower for the answer. Good luck!

## Wednesday, December 10, 2008

### Round 290

Advent Calendar NP rewards:

Day 1: 324 NPs

Day 2: 945 NPs

Day 3: 394 NPs

Total: 324 + 945 + 394 = 1663 NPs

Day 4: 295 NPs

Day 5: 953 NPs

Day 6: 279 NPs

Total: 295 + 953 + 279 = 1527 NPs

Day 7: 273 NPs

Day 8: 479 NPs

Day 9: 374 NPs

Total: 273 + 479 + 374 = 1126 NPs

Day 10: 179 NPs

Day 11: 278 NPs

Day 12: 639 NPs

Total: 179 + 278 + 639 = 1096 NPs

Day 13: 730 NPs

Day 14: 579 NPs

Day 15: ? NPs

Total: 730 + 579 + ? = 1309 + ? = ? NPs

Good luck :)

## Wednesday, November 26, 2008

### Next round

The question is read backwards from the remaining letters:

"what is the numeric deactivation code for the evil program dr sloth created?"

Check step 24 of the below link

http://www.neopets.com/space/npv2_solution.phtml

(Please submit the answer with no spaces or punctuation)

## Wednesday, November 19, 2008

### Round 288

Shah

Roo

Ee

http://www.neopets.com/pronounce.phtml

check out the first four pets then you know the next one... :)

## Wednesday, November 12, 2008

### Round 287

Tier 1: r1 = d1/2 = 6 in (bottom)

Tier 2: r2 = d2/2 = 5.25 in (middle)

Tier 3: r3 = d3/2 = 4.5 in (top)

Height: h = 1.5 in (height of a layer)

V(cake) = pi * ((r1-1/3)^2 + (r2-1/3)^2 + (r3-1/3)^2) * (3*h)

V(frost_side) = pi * (2/3 r1 + 2/3 r2 + 2/3 r3 - 1/3) * (3*h+1/2)

V(frost_top) = pi * (r1^2 + r2^2 + r3^2) * 1/3

V(frost) = V(frost_top) + V(frost_side)

V(jam) = pi * ((r1 - 1/3)^2 + (r2 - 1/3)^2 + (r3 - 1/3)^2) * 1/2

weight = V(cake) * 0.35 + V(frost) * 0.48 + V(jam) * 0.6

cal = weight * 53.4

Remember not to round before the the final answer. Good luck.

## Wednesday, November 5, 2008

### Round 286

Your choice of submission

## Wednesday, October 29, 2008

### Round 285

Acara: 7

Aisha: 7

Blumaroo: 19

Bori: 12

Bruce: 7

Buzz: 10

Chia: 13

Chomby: 39

Cybunny: 11

Draik: 55

Elephante: 42

Eyrie: 22

Flotsam: 8

Gelert: 18

Gnorbu: 8

Grarrl: 9

Grundo: 9

Hissi: -1

Ixi: 21

Jetsam: 5

JubJub: 12

Kacheek: 15

Kau: 5

Kiko: 13

Korbat: 9

Kougra: 7

Krawk: 6

Kyrii: -2

Lenny: 9

Lupe: 11

Lutari: 3

Meerca: 15

Moehog: 13

Mynci: 35

Nimmo: 19

Orgin: 20

Peophin: 20

Poogle: 19

Pteri: 3

Quiggle: 18

Ruki: 8

Scorchio: 25

Shoyru: 10

Skeith: 12

Techo: 13

Tonu: 13

Tuskanniny: 26

Uni: 13

Usul: 23

Wocky: 11

Xweetok: 31

Yurble: 13

Zafara: 1

## Wednesday, October 22, 2008

### Round 284

http://www.mste.uiuc.edu/users/exner/ncsa/base/

I found that the following is match:

553 (base 13)

546 (base 23)

897 (base 17)

318 (base 19)

converts all 4 numbers into base 10 and sum them up then convert back to the base 32 and submit the answer.

This is where you can learn about base:

http://en.wikipedia.org/wiki/Base_(mathematics)

## Wednesday, October 15, 2008

### Round 283

If there is no tricks, you shouldn't need hints? or would you... ?

Some people suggest this one:

http://en.wikipedia.org/wiki/Answer_to_life_the_universe_and_everything#Arthur.27s_Scrabble_tiles

Logically, I don't really see the reason for it but feel free to answer what you like. Maybe it is the answer.... We never know...

## Thursday, October 9, 2008

### Round 282

Date Rewarded: October 16th, 2008.

As you may know, each Neopets item has a numerical rarity associated with it. So add up the following:

The rarity of the item awarded in Lenny Conundrum #92

+ The rarity of the item awarded in Lenny Conundrum #107

+ The rarity of the item awarded in Lenny Conundrum #129

+ The rarity of the item awarded in Lenny Conundrum #142

+ The rarity of the item awarded in Lenny Conundrum #192

+ The rarity of the item awarded in Lenny Conundrum #219

+ The rarity of the item awarded in Lenny Conundrum #229

+ The rarity of the item awarded in Lenny Conundrum #281

**What is the total?** If a rarity has changed since the prize was first awarded, go with the *current* rarity. And please, submit only a number with no punctuation or other information.

__Autumn Leaf Wreath__

__Click to show/hide hints__

## Thursday, October 2, 2008

### Round 281

Date Rewarded: October 9th, 2008.

Walking into Chesterdrawer's Antiques, you notice several clocks on the wall. The first clock reads 9:00, the second reads 6:07, the third 10:45, the fifth 7:45, the sixth 7:52, and the seventh 4:37.

**What should the fourth clock read?**

__Grandfather Clock__

__Click to show/hide solution__

First we convert the clock time into position of hour and minute hands of 12 hour dial face. Then, we use the Flag Semaphore Character chart [1] to decode the hands.

A | B | C | D | E | F |

G | H | I | J | K | L |

M | N | O | P | Q | R |

S | T | U | V | W | X |

Y | Z |

9:00 => P

6:07 => E

10:45 => O

(the 4th clock)

7:45 => H

7:52 =>I

4:37 => N

The word would be PEOPHIN (which is a name of a pet species). Therefore, the 4th letter is P which is the same as the first one. The answer is 9:00.

__Results__: 1885 people guessed the correct answer earning themselves

**1062 NP**each.

References:

[1] Flag Semaphore Characters

## Thursday, September 25, 2008

### Round 280

Date Rewarded: October 2nd, 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 a

_{1}is the first digit (after the decimal point) of Pi, a

_{2}is the second digit, and so on...

What would the following formula equal:

_{1}- a

_{2}) * (a

_{2}- a

_{3}) * (a

_{3}- a

_{4}) * ... * (a

_{99}- a

_{100})

**What is the answer?**

__Flatfruit Table__

__Click to show/hide hints__

The numerical value of PI truncated to 100 decimal places [1] is:

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679

We notice that a

_{24}= a

_{25}= 3. Therefore the formula equal to:

_{1}- a

_{2}) * (a

_{2}- a

_{3}) * ... * (a

_{23}- a

_{24}) * 0 * (a

_{25}- a

_{26}) * ... * (a

_{99}- a

_{100}) = 0

There are several other pairs of consecutive digits that are the same. The answer is 0.

__Results__: 6249 people guessed the correct answer earning themselves

**321 NP**each.

References:

[1] Decimal expansion of PI

## Thursday, September 18, 2008

### Round 279

Date Rewarded: September 25th, 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.

Add up all of the previous Lenny Conundrum answers where the answer could be expressed as a number. If the answer was more than one number, pick the lower of the two answers. Take the square root of that sum, round to the nearest integer, and replace the digits as follows:

1 : G

2 : A if preceded by an odd digit, P if preceded by an even digit

3 : H if preceded by an odd digit, R if preceded by an even digit

4 : T if preceded by an odd digit, Y if preceded by an even digit

5 : O if preceded by an odd digit, E if preceded by an even digit.

6 : N

7 : D

8 : U if preceded by an odd digit, I if preceded by an even digit.

9 : S if preceded by an odd digit, W if preceded by an even digit.

0 : L if preceded by an odd digit, M if preceded by an even digit.

Then, unscramble these letters to find a Neopian word. **What is the word?** Please only submit a single word, with no other information or punctuation, or your answer may be disqualified.

__Rainbow Arm Chair__

__Click to show/hide solution__

The biggest number that can contribute to the sum is in Round 111 (294,215,686,440,197,000,000), the second biggest number is in Round 269 (52,907,904,000). Other numbers are insignificant to the biggest number. If we take the square root of the biggest number, we get 17,152,716,591. If we take the square root of the sum of the two biggest numbers, we get 17,152,716,592. Therefore, other numbers do not affect the result. It has been verified by adding all numbers in all rounds.

Using 17,152,716,592 to decode, we get GDGOADGNESA. It is not supposed to be what TNT intended. It should be GDGAADGMESA or GDGMADGAESA. With either one of them, the answer is gadgadsgame. Here is what TNT said:

Actually, there was an error in the puzzle that we did not notice until after the Lenny Conundrum went live, so we accepted many different answers that had "Gadgads" in it.

__Results__: 1325 people guessed the correct answer earning themselves

**1510 NP**each.

## Thursday, September 11, 2008

### Round 278

Date Rewarded: September 18th, 2008.

**What percentage of users answering this question will get it correct?**

Please round to the nearest whole number. Please do not include any characters in your answer other than numbers. This includes spaces, punctuation, or percentage signs. If there is no correct answer, we'll pick whatever answer comes closest to being correct. And yes, we're intentionally asking this question again.

__Funky Blue and Orange Sofa__

__Click to show/hide solution__

Another guessing game. Last week answer is 3 so a lot of people went with 3. Here is the solution from TNT

19,427 users entered this week's Lenny Conundrum. Here were the top twelve answers, with the rounded percentage of users answering each one:

- "3" (2517 guesses, 13.0% of total entries)
- "5" (1498 guesses, 7.7% of total entries)
- "4" (1429 guesses, 7.4% of total entries)
- "100" (1258 guesses, 6.5% of total entries)
- "2" (1244 guesses, 6.4% of total entries)
- "1" (924 guesses, 4.8% of total entries)
- "6" (505 guesses, 2.6% of total entries)
- "7" (444 guesses, 2.3% of total entries)
- "50" (431 guesses, 2.2% of total entries)
- "0" (418 guesses, 2.2% of total entries
- "10" (402 guesses, 2.1% of total entries
- "8" (226 guesses, 1.2% of total entries

All other guesses came in at under 2%, and since 0, 1, and 2 are already accounted for in the top ten, it's just a matter of which one comes closest. From above, you can see that "0" came closest to its corresponding percentage, so 0 was the correct answer.

__Results__: 418 people guessed the correct answer earning themselves

**4785 NP**each.

## Thursday, September 4, 2008

### Round 277

Date Rewarded: September 11th, 2008.

**What percentage of users answering this question will get it correct?**

Please round to the nearest whole number. Please do not include any characters in your answer other than numbers. This includes spaces, punctuation, or percentage signs. If there is no correct answer, we'll pick whatever answer comes closest to being correct.

__Pink Lenny Painting__

__Click to show/hide solution__

It is a guessing game. The following is the solution from TNT.

19,948 users entered this week's Lenny Conundrum. Here were the top ten answers, with the rounded percentage of users answering each one:

- "100" (1370 guesses, 6.9% of total entries)
- "1" (1141 guesses, 5.7% of total entries)
- "3" (821 guesses, 4.1% of total entries)
- "0" (766 guesses, 3.8% of total entries)
- "2" (668 guesses, 3.4% of total entries)
- "50" (654 guesses, 3.3% of total entries)
- "5" (571 guesses, 2.8% of total entries)
- "10" (525 guesses, 2.6% of total entries)
- "4" (460 guesses, 2.3% of total entries)
- "100%" (366 guesses, 1.8% of total entries, but DISQUALIFIED since the question stated to omit percentage signs)

All other guesses came in at under 2%, and since 0, 1, and 2 are already accounted for in the top ten, it's just a matter of which one comes closest. From above, you can see that "3" came closest to its corresponding percentage, so 3 was the correct answer. Wouldn't be interesting to see how people would answer this question already knowing how people answered it before?

__Results__: 821 people guessed the correct answer earning themselves

**2437 NP**each.

## Thursday, August 28, 2008

### Round 276

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.

__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.

## Thursday, August 21, 2008

### Round 275

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?

__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.

## Thursday, August 14, 2008

### Round 274

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.

__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:

Therefore, the answer is 422.

__Results__: 1432 people guessed the correct answer earning themselves

**1397 NP**each.

## Thursday, August 7, 2008

### Round 273

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.

__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.

## Thursday, July 24, 2008

### Round 272

Date Rewarded: July 31st, 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 four numbered tiles, one with a 3 on it, one with a 4, one with a 5, and one with a 6.

**What is the largest four-digit number that can be formed by these tiles that is not evenly divisible by 9?** Only submit a four-digit number as your answer; any other information may disqualify your entry.

__Faerie Tales: Cloud Nine__

__Click to show/solution__

A number is divisible by 9 when the sum of its digits is divisible by 9 [1]. If we sum the four given digits: 3 + 4 + 5 + 6 = 18 (which is divisible by 9), there can't be a number of those 4 digits that isn't divisible by 9.

However, if you rotate the #6 tile, you get #9. Now, the sum of the digits is 3 + 4 + 5 + 9 = 21 (which is not divisible by 9). Any 4 digit number that formed by the above digits will not be divisible by 9. Therefore, the answer is the largest number formed by those 4 digits (3, 4, 5, 9). It is 9543.

__Results__: some (5503-5517) people guessed the correct answer earning themselves 363

**NP**each.

References:

[1] Divisibility rule

## Thursday, July 17, 2008

### Round 271

Date Rewarded: July 24th, 2008.

Assume the world of Neopia is a spherical planet with a diameter of 1600 km with a uniform density of 5200 kilograms per cubic metre. If the moon of Kreludor is in a geostationary orbit around Neopia, and assuming a Neopian sidereal day is exactly 24 hours, how far is that geostationary orbit above the surface of Neopia?

Please submit your answer in kilometres, and round to the nearest kilometre. Submit only a number; any additional information may disqualify your entry.

__Kreludan Defender Plushie__

__Click to show/hide solution__

This puzzle is about Geostationary orbit. You can find a full explanation about this topic in [1]. The main equation we need to focus on is:

^{3}= G*M / ω

^{2}

where r is the distance between the Neopia's center of mass to the Kreludor moon's geostationary orbit, G = 6.674 28 * 10

^{-11}m

^{3}/(kg*s

^{2}) is the gravitational constant, M is the mass of the Neopia and ω is the angular speed of the moon.

The mass of the Neopia planet can be calculated by the following equation:

^{3}

where ρ = 5200 kg/m

^{3 }is the density of Neopia, V is the volume of the planet, R = d/2 = 800 km = 800,000 m is the radius of the planet.

The angular speed of the Kredulor moon can be calculated by the following equation:

Therefore, we have:

^{3}= G * ρ * 4/3 * pi * R

^{3}/ (pi/43200)

^{2}= (86400)

^{2}* G * ρ * R

^{3}/ (3*pi)

We use 1000 factor in the above equation because we want to get in kilometers. Round the distance and we get 4402 as the answer.

__Results__: 526 people guessed the correct answer earning themselves

**3803 NP**each.

References:

[1] Geostationary orbit

## Thursday, July 10, 2008

### Round 270

Date Released: July 10th, 2008.

Date Rewarded: July 17th, 2008.

The Monoceraptor was walking down a path one day when a Babaa appeared in front of it at exactly 8:06 AM.

The next day, the Monoceraptor was walking down the same path, and the Babaa appeared in front of it at 6:03 PM.

The next day, the same thing happened at 11:05 AM.

The next three days were at 3:09 PM, 5:05 AM, and 4:01 AM.

**What time did the Babaa appear in front of the Monoceraptor on the seventh day?** Submit your answer in the exact same time format as above. For example, if it occured at 9:15 in the evening, you would submit **9:15 PM**. Do not include any extra information other than your answer.

__Grandfather Clock__

__Click to show/hide solution__

This is a sequence puzzle. The sequence is: 8:06 AM, 6:03 PM, 11:05 AM, 3:09 PM, 5:05 AM, 4:01 AM.

If we write twenty four hours in words and arrange in alphabetical order, it should be: eight (8 AM), eighteen (6 PM), eleven (11 AM), fifteen (3 PM), five (5 AM), four (4 AM), fourteen, nine, nineteen, one, seven, seventeen, six, sixteen, ten, thirteen, three, twelve, twenty one, twenty three, twenty two, two, zero. Therefore, the next hour should be fourteen or 2 PM.

For the minutes, notice the PI number: 3.14159265358979323846... The 8th digit is 6, the 18th digit is 3, the 11th digit is 5, the 15th digit is 9, the 5th digit is 5 and the 4th digit is 1. Therefore, the next minute should be corresponding to the 14th digit which is 7.

The answer is 2:07 PM.

__Results__: 50 people guessed the correct answer earning themselves

**40,000 NP**each.

## Thursday, July 3, 2008

### Round 269

Date Rewarded: July 10th, 2008.

The Monoceraptor was walking down a path one day when a babaa appeared in front of it. "Solve this puzzle, and you may pass," it said.

Another ancient tomb in the Lost Desert has the following grid engraved on the tomb door:

You must fill in each empty square with a digits from 1-9 such that the vertical sums of the digits match the number above the column, and the horizontal sums match the numbers to the left of the row. No digit will be used more than once in a set. Once you figure out the digits, multiply all of the digits in the circled squares to get your answer.

**What number will you get when you multiply the circled digits?** Please submit only a single number as your answer; do not submit ANY information other than the answer. Otherwise, your submission may be disqualified.

__Babaa Lamp__

__Click to show/hide solution__

This conundrum is actually a Kakuro game [1]. There is a flaw though. If you look at the upper left part with the red number 17. In second row, you have the sum is 21 with 6 blocks. The only choice for the numbers should be 1, 2, 3, 4, 5 and 6. In the fifth column, you have the sum is 17 with 2 blocks. The only choice for the numbers should be 8 and 9. There is no intersection between the above two sets of numbers. Therefore, either number 17 or number 21 should be corrected. People said that TNT intended to make the mistake to prevent people input numbers into a solver.

If we correct the red number 17 by number 4, then we can solve the grid as following:

There are two choices for the numbers that marked with 'X'

If you multiply the numbers in orange color blocks:

^{2}* 3

^{5}* 4

^{2}* 5

^{3}* 6 * 7 * 8 * 9

^{2}= 52907904000

__Results__: 1536 people guessed the correct answer earning themselves

**1303**

**NP**each.

References:

[1] Kakuro

The prize for each round and its rarity are below:

Round 92 - Happy Birthday Negg (rarity 89)

Round 107 - Filamen (rarity 89)

Round 129 - Ice Scimitar (rarity 87)

Round 142 - Baby Rattle (rarity 92)

Round 192 - Large Chia Cake (rarity 90)

Round 219 - Wartroot Snorkle Lollypop (rarity 82)

Round 229 - Quill and Ink (rarity 91)

Round 281 - Grandfather clock (rarity 90)

Note: Brain Tree Mace is not a correct prize for round 107.

The answer is the sum of all rarity numbers.