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Yeah, I'm going to pass on this.
Math = not my forte
Here's an interesting problem for you...
Find the value of x such that the following is true:
123 (base x) = 18 (base 10)
Yeah, I'm going to pass on this.
Math = not my forte
in my youth...i'm out of practice....
well, i just refreshed my memory, and i'll guess x=-5 or x=3.
123 base x = 18
translates to
1*x^2 + 2*x^1 + 3*x^0=18
x^2+2x+3=18
x^2+2x-15=0
(x+5)(x-3)=0
x=-5, 3
if i'm wrong...nevermind....
bigzak is very close...but he's not done yet.
what do you me to do? box my answer?
seriously. gimme a nudge teach.
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here i have one too...from mensa....
how many cubic yards of dirt are in a hole that is 3 ft x 3 ft x 6ft?
Nudge: There's only one answer.what do you me to do? box my answer?
seriously. gimme a nudge teach.
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here i have one too...from mensa....
how many cubic yards of dirt are in a hole that is 3 ft x 3 ft x 6ft?
Dirt: None. There's no dirt in a hole.
It's 3, because how are you going to have a negative base, since base to any even power is positive? It would leave lots of gaps in the integers.
The answer is not 3.
The number 123 can't exist in base 3 (base 3 has no digit 3).
Therefore, the answer must be -5.
Using the normal rules of base conversion, it can be shown to be true:
1*(-5)^2 + 2*(-5) + 3 = 25 - 10 + 3 = 18.
Actually, I believed as you did, that a negative base was meaningless. A little research corrected my misconceptions.
One side effect of a negative base is that what we call negative numbers are in fact represented by positive numbers. You keep track by noting the number of digits...an odd number of digits and the number is positive; even number of digits, negative.
In fact, any number can be used as a base. It doesn't even have to be rational.
.. my bad. My brain doesn't function correctly before 11 I think.
Now I recall why I hate math so much.
I've been told the same thing. Unfortunately I get to work about 6... my bad. My brain doesn't function correctly before 11 I think.
Well, if you count in base (pi), you really can say that math is an irrational subject...
Thank God for computers.
Dirt: None. There's no dirt in a hole.
travis, you . you could have let some of the non-nerds take a guess.... :p
You been talking to Jenn or something?
I didn't know the question wasn't for me...you were talking to me, and so I just assumed...travis, you . you could have let some of the non-nerds take a guess.... :p
it's all good trav...i'm just talkin ...good job!
OK... what is the remainder of 14 to the 763265 power when divided by 37?
I.e., 14^763265 mod 37
May I assume base 10?
Yeah... show your work too
First, factor 763,265 in binary:
2^20 = (2^10)^2 = 1024^2 = (1000+24)(1000+24) = 1,000,000 + 2 * 24,000 + 24^2
= 1,048,000 + 24^2 = 1,048,000 + (20+4)(20+4) = 1,048,000 + (400+ 2 *4 * 20 + 16)
= 1,048,000 + (400 + 160 + 16) = 1,048,576 > 763,265
2^10 = 1024 < 763,265
2^15 = 2^10 * 2^5 = 1024 * 32 = (1000+24)*(30+2) = 30,000 + 2000 + 720 + 48
= 32,768 < 763,265
2^17 = 2^15 * 2^2 = 32,768 * 4 = 32,768 * (2+2) = 65,536 + 65,536 = 131,072 < 763,265
2^18 = 2^17*2 = 262,144 < 763,265
2^19 = 2^18 * 2 = 524,288 < 763,265
Therefore, 2^19 is the largest power of 2 that fits into 763,265
763,265 - 2^19 = 763,265 - 524,288 = 238,977
Ie, 763,265 = 2^19 + 238,977
By our previous work, the power we're looking for is greater than or equal to 17 and less than 18 since 2^18 > 238,977 and 2^17 < 238,977
therefore, 2^17 is the largest power of 2 that fits into 238,977
238,977 - 2^17 = 238,977 - 131,072 = 107,905
Ie, 763,265 = 2^19 + 2^17 + 107,905
By our work in doing the binary search for 19, the biggest power of 2 that can fit into 107,905 is less than 2^17 (since 2^17 > 107,905), and greater than or equal to 2^15 since 2^15 < 107,905
2^16 = 65,536 < 107,905, so 2^16 is the largest power of 2 that can git in 107,905
107,905 - 2^16 = 107,905 - 65,536 = 42,369
Therefore, 763,265 = 2^19 + 2^17 + 2^16 + 42,369
By the same technique, we see 2^15 is the largest power of 2 that fits into 42,369 is 2^15
42,369-2^15 = 42,369 - 32,768 = 9,601
Therefore, 763,265 = 2^19 + 2^17 + 2^16 + 2^15 + 9,601
2^15 = 32,768 > 9,601 and 2^10 = 1,024 < 9,601
2^12 = 2^10 * 2^2 = 2^10 * 4 = (1025 -1 ) * 4 = 4100 - 4 = 4,096 < 9,601
2^13 = 2^12 * 2 = 8,192 < 9,601
Therefore, 2^13 is the largest power of 2 that fits into 9,601
9,601 - 2^13 = 9,601 - 8,192 = 1,409
Therefore, 763,265 = 2^19 + 2^17 + 2^16 + 2^15 + 2^13 + 1,409
Do another binary search... 2^10 = 1,024 < 1,409, 2^12 = 8,192 > 1,409
2^11 = 2,048 > 1,409
Therefore, 2^10 is the largest power of 2 that fits into 1,409
1,409 - 2^10 = 1,409 - 1,024 = 385
Therefore, 763,265 = 2^19 + 2^17 + 2^16 + 2^15 + 2^13 + 2^10 + 385
Do a binary search for the biggest power of 2 that fits into 385:
2^10 = 1,024 > 385, 2^5 = 32 < 385 ==> exponent is >= 5, less than 10
2^7 = 4 * 2^5 = 128 < 385
2^8 = 2*128 = 256 < 385
2^9 = 512 > 385
Therefore, 2^8 is the largest power of 2 that fits into 385
385 - 2^8 = 385 - 256 = 129
Therefore, 763,265 = 2^19 + 2^17 + 2^16 + 2^15 + 2^13 + 2^10 + 2^8 + 129
129 = 128 + 1 = 2^7 + 1 = 2^7 + 2^0
Therfore, 763,265 = 2^19 + 2^17 + 2^16 + 2^15 + 2^13 + 2^10 + 2^8 + 2^7 + 1
763,265 = 2^16 * (2^3 + 2 + 1) + 2^8 *( 2^7 + 2^5 + 2^2 + 1) + 2^4 * 2^3 + 1
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14^763265 mod 37 = 14^(2^16 * (2^3 + 2 + 1) + 2^8 *( 2^7 + 2^5 + 2^2 + 1) + 2^4 * 2^3 + 1) mod 37
= 14^(2^16 * (2^3 + 2 + 1)) * 14^(2^8 *( 2^7 + 2^5 + 2^2 + 1)) * 14^(2^7) * 14 mod 37
14 ^ 2 mod 37 = (10+4)*(10+4) mod 37 = (100 + 80 + 16) mod 37 = 100 mod 37 + 80 mod 37 + 16 mod 37 = 26 mod 37 + 6 mod 37 + 16 mod 37 = ( 32 + 16 ) mod 37 = 11
14^4 mod 37 = 11^2 mod 37 = 121 mod 37 = 10
14^8 mod 37 = 10^2 mod 37 = 100 mod 37 = 26
14^16 mod 37 = 26^2 mod 37 = ((20+6)*(20+6)) mod 37
= (400 + 240 + 36) mod 37 = 400 mod 37 + 240 mod 37 + 36 mod 37
= 30 mod 37 + 18 mod 37 + 36 mod 37
= (30 + 18 + 36) mod 37 = (30 + 17) mod 37 = 10
14^32 mod 37 = 10^2 mod 37 = 26
14^64 mod 37 = 26^2 mod 37 = 10
14^128 mod 37 = 10^2 mod 37 = 26
ie, 14 ^ (2^k) mod 37 = {10 if k even; 26 if k odd}
Since 763,265 = 2^19 + 2^17 + 2^16 + 2^15 + 2^13 + 2^10 + 2^8 + 2^7 + 1,
14^763,265 = 14 ^ (2^19 + 2^17 + 2^16 + 2^15 + 2^13 + 2^10 + 2^8 + 2^7 + 1)
= 14^(2^19) * 14^(2^17) * 14^(2^16) * 14 ^(2^15) * 14^(2^13) * 14^(2^10) * 14^(2^8) * 14^(2^7) * 14
Therefore, 14^763,265 mod 37 = 26 * 26 * 10 * 26 * 26 * 10 * 10 * 26 * 14 mod 37
26 * 26 * 10 * 26 * 26 * 10 * 10 * 26 * 14 mod 37
= (26 * 26) * 10 * 26 * 26 * 10 * 10 * 26 * 14 mod 37
= (10) * 10 * 26 * 26 * 10 * 10 * 26 * 14 mod 37
= (10 * 10) * 26 * 26 * 10 * 10 * 26 * 14 mod 37
= (26) * 26 * 26 * 10 * 10 * 26 * 14 mod 37
= (26* 26) * 26 * 10 * 10 * 26 * 14 mod 37
= (10) * 26 * (10 * 10) * 26 * 14 mod 37
= (10) * 26 * (26) * 26 * 14 mod 37
= (10) * (26*26) * 26 * 14 mod 37
= (10) * (10) * 26 * 14 mod 37
= (10*10) * 26 * 14 mod 37
= (26) * 26 * 14 mod 37
= (26*26) * 14 mod 37
= (10) * 14 mod 37
= (10*14) mod 37
= 140 mod 37
Therefore, 14^763265 mod 37 = 140 mod 37 = (37*3 + 29) mod 37 = 29
ie, the remainder of 14^763265 / 37 is 29
there just aren't enough math s out there these days.
All the women I talk to who are impressed by math skills are conservative asians who don't on the first date.
Yeah, but depending on how you work out a deal with a hooker, you might be able to get her to pay you...
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