So judging by the notebook (*cough* sorry, doodle pad. Note pad implies notes) this was in and the page it was on, I was 16, so summer 2000. I figured this mostly from the X-wing 3 pages ahead and the scotch mint predicting I passed my written drivers test. It was right, very smart things mints.
Anyways, apparently I was trying to figure out the square root of purple. And failed. (That course was the most boring thing in my life.)
So skip ahead to now and I tried it again. I got 4 answers this time, either I'm smarter, or more creative, I'll take either...Then searching the internet I found dozens of answers, obviously this is a very important question. I also found out that while violet exists, purple is actually a figment of our minds as it is always a mixture of at least 2 other colors. How cool is that! How deeply philosophical when we consider the context of this page.
Answer 1: Purple is a RGB Hex Number
Since I'm writing online, this was obvious. Purple is 50% red, 0% green, and 50% blue. So:
- Red = 50% = 128d = 80h
- Green = 0% = 0d = 00h
- Blue = 50% = 128d = 80h
- RGB(purple) = 800080h
X = sqrt(800080h) = sqrt(8388736d) = 2896.33d = B50h
What color is B50? This putrid tawny orangey mess:
Answer 2: Purple is a RGB Number
Similar, but we will be taking the square root of each value.
- Red = 50% = 128
- Green = 0% = 0
- Blue = 50% = 128
R = sqrt(128) = 11.31
G = sqrt(0) = 0
B = sqrt(128) = 11.31
What color is 11.3, 0, 11.3? Very near black (the right half is true black for comparison):
Tangent A
What do we get if we average our first 2 answers?
- Answer 1 = B50h
- Answer 2 = 11, 0, 11 = 0B000Bh
- Sum = 0B0B5Bh = 723803d
Average = 723803d / 2 = 361901.5d = 585AEh
Answer 3: Purple is 6 Letters Replacing Numbers
Now, we are going to assume that they are all single digit numbers. Obviously the letters can not equal each other.
- P = P = ?
- U = ?
- R = ?
- L = ?
- E = ?
- Max 6 digits
- Maximum number is 987965
- Minimum number is 012034
Assumption #2 is that we want an integer as an answer. So, our possible factors are everything from 110² (12100) up to 993² (986049). Ugg. Well if the 2 'P' positions are different, then that number fails. So that narrows it down to 96 numbers.
Now we can eliminate the answers that have variables equaling the same number (P = L is a no-no). We end up with 17 answers :)
- 047089 = 217² = ??R
- 051076 = 226² = ??E
- 067081 = 259² = ???
- 093025 = 305² = RPE
- 197136 = 444² = ???
- 234256 = 484² = R?R
- 267289 = 517² = ??R
- 320356 = 566² = LEE
- 389376 = 624² = E??
- 426409 = 653² = R??
- 498436 = 706² = ??E
- 625681 = 791² = ??E
- 675684 = 822² = L??
- 680625 = 825² = ULE
- 802816 = 896² = P?E
- 820836 = 906² = ?RE
- 938961 = 969² = PLP
RPE? LEE? ULE? PLP?, Nothing truely satisfying in there eh? (he he, I said 'eh'). I guess 896 could be PIE. Hmmm, if you stretch a bit further:
- ??E could be AXE
- E?? could be ETC or ELK
- L?? could be LAN
- ?RE could be ORE or ARE
Not much better. I think ELK might be the best, followed closely by ETC and PIE (except that PIE sounds like pi).
Answer 4: Purple is 6 Variables
Now, we are going to again assume that they are all single digit numbers. And again the letters can not equal each other. This time we are also banning zero from our equation.
- P*U*R*P*L*E
- Maximum number is 9 x 9 x 8 x 7 x 6 x 5 = 136080
- Minimum number is 1 x 1 x 2 x 3 x 4 x 5 = 120
Assumption #2 is that we want an integer as an answer (like before). There are a mere 358 possible answers now, everything from 11² (121) up to 368² (135424).
The final answer will be even because it's square will be even. Why? Because the only way you can have an odd square is if all the factors are odd. Any combination of 1, 3, 5, 7, 9 won't root evenly in our case, so we are down to 179 possibilities.
- 1 x 1 x 3 x 5 x 7 x 9 = 945
- 1 x 3 x 3 x 5 x 7 x 9 = 2835
- 1 x 3 x 5 x 5 x 7 x 9 = 4725
- 1 x 3 x 5 x 7 x 7 x 9 = 6615
- 1 x 3 x 5 x 7 x 9 x 9 = 8505
Can we narrow it down more? Yes. Remember, we want the square root right? So therefore there are exactly 2 of every number, thus 2 of each factor. For example our first candidate number is 12 who has the factors of 2, 2, and 3. So when we square 12 we have the factors of 2, 2, 3, and 2, 2, 3. If we take 20, we would have the factors 2, 2, 5, and 2, 2, 5.
So what? A lot actually. Since we can only have 1 duplicate factor, and all factors have to be under 10, we have to change the extras. Like so:
- 12² = 2, 2, 2, 2, 3, 3 = 2, 4 (2x2), 6 (2x3), and 3 - GOOD
- 14² = 2, 2, 7, 7 = 2, 7, and 14 (2x7) - NO GOOD
- 16² = 2, 2, 2, 2, 2, 2, 2, 2 = 2, 4 (2x2), 8 (2x2x2), 2, and 2 - NO GOOD
- 18² = 2, 2, 3, 3, 3, 3 = 2, 6 (2x3), 3, and 9 (3x3) - GOOD
Excellent, a pattern. Anything with a factor greater than 3 can be eliminated. We will deal with too many 2's and 3's next. First of all, we are down to 20 possibilities!
Now then, using 2 and 3 (and 1), what can our possible values for our variables be? Well there is 1, 2, and 3. Simple multiplication makes 4, 6, and 9. Finally there is 8. So we have seven possible values (1, 2, 3, 4, 6, 8, 9) and we need to use 5 at any one time.
Now we will deal with having to much of a good thing.
- If there are no 3's, we can't have more than six 2's (2, 2x2, and 2x2x2).
- If there are no 2's, we can't have more than three 3's (3, and 3x3).
- If there are 2's and 3's, we can have one more 2 (2x3) for a total of 7.
- If there are 2's and 3's, we can have one more 3 (2x3) for a total of 4.
- 16, 32, 64, 128, and 256 are out because of rule 1
- 48, 96, 128, 144, 192, and 288 are out because of rule 3
- 54, 108, 162, 216, and 324 are out because of rule 4
We are down to 5 possible answers. Our first answer is 12 (1 x 2 x 3 x 1 x 4 x 6 = 144). The first 4 answers are:
- 12² = 144 = 1 x 2 x 3 x 1 x 4 x 6
- 18² = 324 = 1 x 2 x 3 x 1 x 6 x 9
- 24² = 576 = 1 x 2 x 4 x 1 x 8 x 9
- 36² = 1296 = 3 x 1 x 2 x 3 x 8 x 9
12 has the nicest feeling to it, in my opinion, so I'll choose it. Mind you, having the square root of purple be one of the requirements for being in Rovers also has appeal. Anyways it's dinner time, so I'll leave you to figure out the last answer (hint: 71 < x < 73).