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~sERgEI pRokofIEv
What is Peter and the Wolf?
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------- ----- + ------ --- = --------- ------ ----
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If (i)^x =i^y, where i= (-1)^1/2 and x, y ∈ Z
Then (|x|+|y|)mod4=0
Cool huh?
I'll be back with more every guess because I'm really bored nowadays
Anyway, speaking of which, I guess i, where i is....the ninth letter of the English Alphabet.
Edit: what's a bouns question again?
Double edit: Oh and before anyone corrects me I'm using the modulus operation in computing to find the remainder of a number; not the one used in number theory. Nice try though
Last edited by Southern Corn on Fri Aug 18, 2017 3:52 pm, edited 2 times in total.
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--i---i ----e + ---i-- --- = --------- e----e ----
Correct guesses: E, I
Wrong guesses: None!
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That's a consequence of i^4 = 1.
Did you know that i^i, an imaginary base with an imaginary exponent, results in a real number?
My guess is N, though.
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--i---i ---ne + ---in- --- = --------- e-c--e ---n
Correct guesses: C, E, I, N
Wrong guesses: None!
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That's a consequence of i^4 = 1.
Did you know that i^i, an imaginary base with an imaginary exponent, results in a real number?
My guess is N, though.
Yeah. Euler's formula and all. Pretty cool, huh?
Anyway, today's random maths facts is about digital roots! Most of y'all probably know about them but to those who don't, well...it's pretty simple. It's the single digit value obtained by the process of summing digits of a non-negative integer continuously. For example, take the number 11429. Its digital root is 8, as 1+1+4+2+9=17, and 1+7=8. For now, let's take the digital root of a non-negative integer n as dr(n).
Anyway, more cool facts:
1. 0 is the only number with a digital root of 0.
2. If (dr(n))mod3=0, then (n)mod3=0. In other words, all non-negative integer multiples of 3 have a digital root of either 3,6,9, and technically 0 as 0 is itself a multiple of 3, and vice-versa.
3. In a somewhat similar fashion, (dr(n))mod9=0, or all multiples of 9 have a digital root.
4. Both 0 & 9 do not change the digital root of the number, so they can be negated when taking it.
Now, let's take two non-negative integers a & b, with digital roots m & n respectively.
5. dr(a+b)=dr(m+n)
In other words, the digital root of the sum of the two numbers is equal to the digital root of the sum of their digital roots (or even just the sum of the digital roots if m+n<10)!
6. dr((a(a+1))/2)=dr((m(m+1))/2)
In other words, the digital root of the sum of the first 'a'th numbers is equal to the digital root of the sum of the first 'm'th numbers.
Pretty cool, huh?
Anyway, guesses, guesses.
I guess a D, for digital root!
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Also I guess T who'd have thought huh?
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Also I guess T who'd have thought huh?
Yeah, it's actually how I knew it originally myself. I never really knew the term for it as Digital Root. We actually have a game over here where you say a number and you're supposed to identify it as either a multiple of 3, a multiple of 5, a multiple of both 3 and 5, or neither. It's actually pretty tricky, but that trick comes in handy.
Also, I've recently developed a tendency to look at the licence plates of vehicles while going home and identify their digital root. It helps kill time. A surprising amount of vehicles had a digital root of 9 actually.
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--i---i p--ne + ---in- --- = ----p---- e-c-pe p--n
Correct guesses: C, E, I, N
Wrong guesses: D, T
|/ |
| ☺
|
|
|
|
========
Oh, Fizzbuzz. I've heard of that game, but never played it. They just did a kind of interesting video on Computerphile about using Fizzbuzz as a programming exercise for an interview question for programmer jobs.
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GDI Lone, you know me too well. Your turn.
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Anyway, unit digits and powers!
1. All powers of zero greater than zero are still equal to zero.
2. Similarly, all powers of one are equal to one.
3. 2 undergoes a continuous loop with the unit digits of its non negative integer powers. 2^1=2,2^2=4,2^3=8,2^4=16... then 32,64,128,256,... they loop around 2,4,8 and 6 respectively.
4. Like 2, 3 has a similar loop:3-9-7-1. 4's powers however are just the even non negative integer powers of 2, aka 4-6. Same with 9, which circles between 9 and 1. Much simpler in comparison.
5. 5 and 6 are by far the simplest of them all, however. The unit digits of their non-negative integer powers are just....themselves. Pretty elementary.
6. 7 has a theme too. It's similar to the loop of 3's powers, but in a different order. 7-9-3-1 instead of 3-9-7-1. In a similar sense, 8 is also just the 2 loop in a different order: 8-4-2-6 instead of 2-4-8-6. Funnily enough, they're even put in a similar mismatched order.
7. That covers all single digit numbers, but i also has a loop! Though it's not the unit digit since it's imaginary. No, the values cycle through as shown:
i^4K=1
i^(4K+1)=i
i^(4K+2)=-1
i^(4K+3)=-i
Where K is an integer.
Anyway, enough rambling. I'm guessing an S for SC is amazing-...? Huh? What the hell, Lone? Stop ninja-ing me like that, dammit!
But I'm still guessing an S preemptively, though.
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Alright, let's see:
------- s-----. ----- ------
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Wibbly wobbly timey-wimey stuff
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100% pure Joy.
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Right Guesses: O, D, B, E, S, U, R, L, U, T
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_ _ _ _ _
_ _ _ _
_ _ _ _ _ _ _ _ _ _
Wibbly wobbly timey-wimey stuff
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100% pure Joy.
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Refrigerate after opening.
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Happy Maria
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_ _ _ _ _ _ S
_ _ _ _ _
S T _ _
T _ _ _ S _ _ _ _ S
[Right: S, T]
[Wrong: A]
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