Round 280

Date Released: September 25th, 2008.
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 a₁ is the first digit (after the decimal point) of Pi, a₂ is the second digit, and so on...

What would the following formula equal:

(a₁ - a₂) * (a₂ - a₃) * (a₃ - a₄) * ... * (a₉₉ - a₁₀₀)

What is the answer?

Prize


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 a₂₄ = a₂₅ = 3. Therefore the formula equal to:

(a₁ - a₂) * (a₂ - a₃) * ... * (a₂₃ - a₂₄) * 0 * (a₂₅ - a₂₆) * ... * (a₉₉ - a₁₀₀) = 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

Round 279

Date Released: September 18th, 2008.
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.

Prize


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.

Round 278

Date Released: September 11th, 2008.
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.

Prize


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:

1. "3" (2517 guesses, 13.0% of total entries)
2. "5" (1498 guesses, 7.7% of total entries)
3. "4" (1429 guesses, 7.4% of total entries)
4. "100" (1258 guesses, 6.5% of total entries)
5. "2" (1244 guesses, 6.4% of total entries)
6. "1" (924 guesses, 4.8% of total entries)
7. "6" (505 guesses, 2.6% of total entries)
8. "7" (444 guesses, 2.3% of total entries)
9. "50" (431 guesses, 2.2% of total entries)
10. "0" (418 guesses, 2.2% of total entries
11. "10" (402 guesses, 2.1% of total entries
12. "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.

Round 277

Date Released: September 4th, 2008.
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.

Prize


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:

1. "100" (1370 guesses, 6.9% of total entries)
2. "1" (1141 guesses, 5.7% of total entries)
3. "3" (821 guesses, 4.1% of total entries)
4. "0" (766 guesses, 3.8% of total entries)
5. "2" (668 guesses, 3.4% of total entries)
6. "50" (654 guesses, 3.3% of total entries)
7. "5" (571 guesses, 2.8% of total entries)
8. "10" (525 guesses, 2.6% of total entries)
9. "4" (460 guesses, 2.3% of total entries)
10. "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.