# Quality Over Quantities

6.1482925535194332784626433, 15, 70, 5388440228181184467208035634811703511875, 45, 1207432478148385373947988/38313917, 15, 70, ?

• oh hey that's me
– Deusovi
Jul 24, 2017 at 17:32
• Pretty bold to label your own puzzle as high-quality :) Jul 24, 2017 at 17:48
• Technically he didn't :P Jul 24, 2017 at 18:08
• Looks mind-blowing at first sight but in fact, this is an excellent 'in-your-face' to Deusovi. Jul 25, 2017 at 15:02

6.1482925535194332784626433

This number appears to be the same as pi (truncated to 26 places), but with eight digits changed. That 26 is suspicious - looking at the changed digits, they're all between one and eight. Taking the nth letter, where n is the position of the digit changed to k, gives LEONHARD.

15, 70

These numbers look like "IS TO".

5388440228181184467208035634811703511875

This number prime factorizes as $3^6\cdot 5^4\cdot 7^8\cdot 11^7\cdot 47^3\cdot 71^1\cdot 73^5\cdot 83^2$. Those exponents range from 1 to 8, and the primes are pretty small. Sort by exponent, then take each prime's index in the list of primes (2 maps to A, 3 to B, 5 to C, 7 to D...), and you get TWO CUBED, which is naturally a clue for EIGHT.

45

45 looks like "AS" in a similar way to how 15 and 70 yielded IS and TO.

1207432478148385373947988/38313917

Dividing this out gives 31514200914210504.0825... . Taking pairs of digits and converting to letters gives "CONTINUED", a hint to look at the continued fraction. The continued fraction for this number is [31514200914210504; 12, 9, 11, 5, 2, 12, 15, 15], and converting those to letters gives "LIKE BLOO", a hint to the word IMAGINARY (a reference to Bloo from the cartoon Foster's Home for Imaginary Friends)

15, 70

IS, TO again.

?

LEONHARD means Euler's number, e.
IMAGINARY means the imaginary unit, i. That means we have "e is to EIGHT as i is to ???", and the answer is INFINITY, another "number" starting with its corresponding letter.

• If it takes 13 hours to get to a partial answer at least you can say the puzzle is nice and hard ;) Jul 25, 2017 at 8:20
• So…? E is to B as I is to ? Jul 25, 2017 at 12:25
• I think the intended interpretation is LEONHARD is to EIGHT as IMAGINARY is to ?, in which case it's NINE (number of letters). Jul 26, 2017 at 2:16
• @Ankoganit I was more thinking about 3-8, 1-6 or E-B, I-G and that 9 fits it too, so answer is g/G/6/9? Probably Jul 26, 2017 at 13:48