Mark:
THREE TOWNS
since 478 > 300 and 302 > 300, the answer must be 46
(I never saw that, wicked.)
turn around
microscope
balanced meal
Rap:
Many roads
I drew this one up as a triangle with A,B & C on the vertices and labeled the direct pathways (legs) as a,b,&c with a from A to B, b from B to C, and c from A to C.
Then 82=a+bc and 62=b+ac
Adding together
144=a+b+bc+ac=a(1+c)+b(1+c)=(a+b)(1+c)
so
(a+b)(1+c)=144
so 1+c is an integral factor of 144
(1+c)={1,2,3,4,6,8,9,12,16,18,24,36,48,72,144}
so
c={0,1,2,3,5,7,8,11,15,17,23,35,47,71,143}
Subtracting 82=a+bc and 62=b+ac
20=a+bc-(b+ac)=a-b+bc-ac=a-b+c(b-a)=a-b-c(a-b)=(a-b)(1-c)=(b-a)(c-1)
(b-a)(c-1)=20
so c-1 is an integral factor 20
(c-1)={1,2,4,5,10,20}
so c={2,3,5,6,11.21}
now
{0,1,2,3,5,7,8,11,15,17,23,35,47,71,143}∩{2,3,5,6,11.21}={2,3,5,11}
so there are four possible solutions for c {2,3,5,11}
c=2 then b+a=144/3=48 and b-a=20/1=20, 2b=68. b=34 and a=14
check if c+ab<300
2+34*14=478 & 478>300?-this is not a solution
c=3 then b+a=144/4=36 and b-a=20/2=10, 2b=46. b=23 and a=13
check if c+ab<300
3+23*13=302 & 302>300?-this is not a solution
c=5 then b+a=144/6=24 and b-a=20/4=5, 2b=29. b=29/2 this is not an integer?-this is not a solution
c=11 then b+a=144/12=12 and b-a=20/10=2, 2b=14. b=7 and a=5
check if c+ab<300
11+7*5=46 & 46<300?-this is a solution
so there are 5 ways to get directly from A to B
7 ways to get directly from B to C
and 11 ways to get directly from A to C
The total number of ways to get from A to C (direct and indirect) are 11(direct)+5*7(indirect)=46
Amazing, simply amazing. Hang in there buddy good things come to those that wait.
Any employers reading this act quickly to sign this guy up.
He then tops it up with:
Balanced diet or square pizza
Turn over or turn around
Microscope
Shari, you must remember her, she is the one who ?'stole' my persona, would like it known that like a fine wine, " I am a totally mature." I think it fair to say she would like you all to grow up and get with the programme. Good for you, have your people ring my people, we must totally do lunch.
I am reliably informed that she will graduate in 2017. Go girl go!
Dadpad & friends:
I mean the opposite of 'good,' but if you change my first letter, you have a religious leader
sinister
My last half is a color, & my first half often contains fluid
..sacred
am a crowning achievement for someone entering a position of high authority. My last six letters mean the same as 'country.'
corination
Your bride is one smart cookie.
"Try, what do you do?"
Basically, as little as possible. Although I have been known to help the Fed's with their enquiries on a number of occasions. Archaeology however is my main passion. No jokes about ?'old bones' please!
If I had to guess, I would say Shari is studying Art/music. DP has yet to make up his mind.
"cotcidrerayte"
(In)A DIRECTORY ETC
(In)A DECOY CRITTER
(In)A TRICE CODE TRY
BILLED
PLAY stop
Podpodpod
TIME
Operator
Take pets
S***(I) is as old as John will be when (I) is twice as old as John was when (I)'s age was half the sum of their present ages. John is as old as (I) was when John was half the age he will be 10 years from now.
How old is (I)
