NeoPets Riddles (Lenny Conundrums) and Answers Here

Dear TAZ,

Congratulations! You have guessed correctly in the Lenny Conundrum game (round 229). You have won 702 NP!

Because you were in the first 250 to guess correctly, you also have been awarded a Quill and Ink, and receive a trophy and the Lenny Conundrum avatar!

Yours Sincerely,
The Neopets Team!


Thanks everyone who helped last week.

if MEEP is a number that can be written on base 5, all the digits have to be less than 5
so the only possible answers are 0000 and 1332

<?php
for ( $M = 0 ; $M < 5 ; ++$M )
for ( $E = 0 ; $E < 5 ; ++$E )
for ( $P = 0 ; $P < 5 ; ++$P ) {
$answer = $M.$E.$E.$P;
if (base_convert($answer,5,10) + base_convert($answer,7,10) == base_convert($answer,8,10)) {
echo $answer.'<br />';
}
}
?>

Thanks kissychick, it makes more since now. I know I won't get a higher trophy, but at least I'll get some neopoints. Thanks!

So even though the answer to the problem is 730. The answer to the question is actually 1332!?!?

I've never been hot for PHP, but nice code.

it was a post bug i dont know what happened
i just disabled html, bbcode and smiles and finally got the right code
sorry but i dont speak english very well

problem with answer 1332
If Meep is 1332 and we follow the math, then it doesn't add up.
(2+15+75+125 = 217) + (2+21+147+343 = 503)
So 217 + 503 = 720
But the math calculation for base 8 is
(2 + 24 + 192 + 512) which = 730

There's a difference of 10. Unless I missed something?

actually 2+21+147+343 is equal to 513

Don't I feel dumb
Thank you for pointing that out. Don't know where my head was ;-)

Yes, because the question was what number is represented by "MEEP," not what the value of MEEP-base8 was.

Thanks kissychick for posting the solution step by step. I still can't get my head around it. I don't remember hearing of a "base" in this way, I've only used it in reference to powers and logs.

The above was an uncredited portion of this article. If you read the article, then you may have a better understanding of the various solutions which have been posted. :wink:


Using the method explained in the article (above), we first note that, since the smallest base is base-5, none of the digits can be a 5 or greater. We have to work with 0, 1, 2, 3, and 4. Also, M cannot reasonably be zero. We will assume that "specific" implies "distinct"; that is, M, E, and P represent three different digits from among our choices.

Converting the base-x expressions into base-10 (that is, "regular") values, we have:

. . . . .(125M + 25E + 5E + P) + (343M + 49E + 7E + P) = 512M + 64E + 8E + P

Simplify:

. . . . .468M + 86E + 2P = 512M + 72E + P

Combine "like" terms, and simplify some more:

. . . . .14E + P = 44M

Note that, since 14 is even and 44 is even, then 14E and 44M will be even. The only way for the last equation above to work is for P then to be even. That is, P must be one of 0, 2, and 4.

Let's work by cases, since we have only five digits from which to choose.

If M = 0, then the leading digit in each number is a zero, which isn't how we write numbers. So M cannot be zero.

If M = 1, then:

. . . . .14E + P = 44

If P = 0, then:

. . . . .14E + 0 = 44

. . . . .14E = 44

. . . . .E = 44/14 = 22/7

This won't work. On to the next sub-case: If P = 2, then:

. . . . .14E + 2 = 44

. . . . .14E = 42

. . . . .E = 42/14 = 3

This will work! M = 1, P = 2, E = 3. Continue checking for any other solutions.

If P = 4, then:

. . . . .14E + 4 = 44

. . . . .14E = 40

. . . . .E = 40/14 = 20/7

This also won't work. Check the next case for M.

If M = 2, then:

. . . . .14E + P = 88

If P = 0, then:

. . . . .14E + 0 = 88

. . . . .14E = 88

. . . . .E = 88/14 = 44/7

No. If P = 2, then:

. . . . .14E + 2 = 88

. . . . .14E = 86

. . . . .E = 86/14 = 43/7

No. If P = 4, then:

. . . . .14E + 4 = 88

. . . . .14E = 84

. . . . .E = 84/14 = 6

But 6 is too large a digit. We've exhausted the sub-cases, so M cannot be 2.

If M = 3, then:

. . . . .14E + P = 132

If P = 0, then:

. . . . .14E + 0 = 132

. . . . .14E = 132

. . . . .E = 132/14 = 66/7

No. If P = 2, then:

. . . . .14E + 2 = 132

. . . . .14E = 130

. . . . .E = 130/14 = 65/7

No. If P = 4, then:

. . . . .14E + 4 = 132

. . . . .14E = 128

. . . . .E = 128/14 = 64/7

No. So M cannot be 3.

If M = 4, then:

. . . . .14E + P = 176

Consider the sub-cases: If P = 0, then:

. . . . .14E + 0 = 176

. . . . .14E = 176

. . . . .E = 176/14 = 88/7

No. If P = 2, then:

. . . . .14E + 2 = 176

. . . . .14E = 174

. . . . .E = 174/14 = 87/7

No. IF P = 4, then:

. . . . .14E + 4 = 176

. . . . .14E = 172

. . . . .E = 172/14 = 86/7

No. So M cannot be 4. There remains only one value to check for M:

If M = 5, then:

. . . . .14E + P = 220

If P = 0, then:

. . . . .14E + 0 = 220

. . . . .14E = 220

. . . . .E = 220/14 = 110/7

No. If P = 2, then:

. . . . .14E + 2 = 220

. . . . .14E = 218

. . . . .E = 218/14 = 109/7

No. If P = 4, then:

. . . . .14E + 4 = 220

. . . . .14E = 216

. . . . .E = 216/14 = 108/7

No.

This exhausts all possible cases, with only one solution found:

. . . . .********************
. . . . .** M = 1, E = 3, P = 2 **
. . . . .********************

Verifying:

. . .1332(base 5) = 1(5^3) + 3(5^2) + 3(5^1) + 2(5^0)
. . . . .= 1(125) + 3(25) + 3(5) + 2(1)
. . . . .= 125 + 75 + 15 + 2 = 217(base 10)

. . .1332(base 7) = 1(7^3) + 3(7^2) + 3(7^1) + 2(7^0)
. . . . .= 1(343) + 3(49) + 3(7) + 2(1)
. . . . .= 343 + 147 + 21 + 2 = 513(base 10)

. . .1332(base 8) = 1(8^3) + 3(8^2) + 3(8^1) + 2(8^0)
. . . . .= 1(512) + 3(64) + 3(8) + 2(1)
. . . . .= 512 + 192 + 24 + 2 = 730(base 10)

. . . . .217 + 513 = 730

So the only solution we found is now confirmed valid.

Please check my work.

Eliz.

Nice job.

In the interest of getting to the solution quickly, after getting to 14E + P = 44M, you could conclude that E = 3*M because E = 44/14M - P/14 (E = 3.143M - 0.071P).

Given the limited choices for each digit, it would follow that M = 1 and E = 3. From there, P is easily computed.

Thanks stapel. I think I now understand how it works.

Yay! That means I got it right =) Thanks everybody! You guys are good at math xD

Good luck everyone =)

so is M = 1, E = 3, P = 2
because i need to know how exactly spell it correctly

With which aspect(s) of the various posted explanations do you disagree? (You must have some quibble, else why ask the question, right?)

Please be specific. Thank you.

Eliz.

so is the answer 1332 or 730
What i mean what is the lenny conundrum answer?
1332 or 730

What does the question ask? Does it ask for the value, in base-10, for the sum of the left-hand side? Or does it ask for the expression represented by "MEEP"?

To figure out what the answer is, look at what the question wants.

Eliz.

I got the avatar and trophy today!
Thanks guys!
Thanks Podogo!