Contest time! First to answer these riddles wins!! (WINNER POSTED!!)

[joae1975]

The first person to solve all four of these questions with the correct answers will win.  I'll ask the winner to give me a list of yoyo's they like.  Based upon that list, I'll decide their prize.  Don't go crazy and ask for an Oxy-Ti, etc., cuz you're not getting one, LOL!
Any questions about the questions?
Well here are the questions:

1.) At 10pm Shirley trurned off the lights in the living room.  Her husband, Bob, who had been reading there, stayed and continued to read for an hour or so.  How was this possible?  (And no, Shiriley and Bob do no live anywhere near the North Pole.)

2.) What number should replace the question mark if the fourth set of numbers follows the same logic as the first three?

37, 10, 82
29, 11, 47
96, 15, 87
42, ? , 15

3.)  See if you can figure out what number should replace the question mark in the following series:

9, 16, 25, 36, ?

4.)  The Yreka Bakery makes fresh bread every morning.  Let's listen in to this morning's business transactions:
      
      a.)  Rachel, the first customer:  "I'll take half of the bread on the shelf, plus half a loaf."
      b.)  Howie, the second customer:  "I'll take half of what you have left, plus half a loaf."
      c.)  Nina, the third customer:  "I'll take half of what you have left, plus half a loaf."
      d.)  Marshall, the fourth customer:  "I'll take half of what you have left, plus half a loaf."
  
  All four customers left the bakery with what amounted to full loaves.  How many loaves of bread did the bakery start with that
  morning?  And how many did each customer take?

GOOD LUCK!!  MERRY CHRISTMAS AND HAPPY NEW YEAR!!!

-Joe E.

[ed]

a. he's blind, reading braille
b. 6
c. 49
d. 23 to start with: 1st customer takes 11.5+.5 leaving 11, 2nd takes 5.5 +.5 leaving 5, 3rd takes 2.5 +.5 leaving 1, 4th takes .5 +.5.

[SuperPokenerd]

I pm'd you.  Are there multiple answers for the last question?  Becuase I got 15 and ed got 23 and both seem to work.  Ed, I'm curious as to how you solved the 4th.  What i did was i defined N to be the number of loaves to start with and then algebraically determined that each person must take (N+1)/2 , (N+1)/4, (N+1)/8, and (N+1)/16 loaves respectively.  Based on my solution, it seems that any number N such that the prime factorization of N+1 involves 16 (2^4) would serve as a viable answer.  In my solution 23 doesn't appear as a viable solution but evidently it works, i'm just curious how you got it.

[nyjaj23]

1.   he was wearing night vision googles.

3.  49

[DrYoYo]

1: He is blind and reading by Braile, OR he is a Night Elf using Night Vision (Thats right, I went there)

2: 6 (add the first to digits and the last two digits, so 4+2=6 and 1+5=6)

3: 49  (increments to next odd number 7, 9,11,13)

4: 23 Loaves, Rachel took 12, Howie took 6, Nina took 3 and Marshal took 1

[DrYoYo]

Dang, beat by Ed!  Thats what I get for printing it out and coming back to answer the questions!

 

[SuperPokenerd]

i hope my pm got there faster.

[djmatz]

I have more or less the same. But my last question is different.
Curious who won

[DrYoYo]

16 could not work.  The key factor was that all customers took whole loaves.  
If we plug 16 into the problem, then:
Rachel would take 8.5, Howie would take 4.25, Nina would take 2.125 and Marshal would have 1.125

I reread your post, about 15.  I had thought you said 16, but I see you indeed said 15 so.....
15 WOULD work,

Rachel would take 8, Howie would take 4, Nina would take 2, and Marshal would take 1

[djmatz]

Damn didnt read the thing about whole loaves. Damn it

[ed]

superpokenerd, just knew it had to start odd and stay odd. estimated 21, but the results went even. 19 wouldn't end whole. 23 was the 3rd i tried. now i'm kinda curious about the properties of numbers that fit this criteria/pattern.

[DrYoYo]

Ed, I think we are both wrong, I went over it again and 12+6+3+1= 22, not 23
Same with yours (11.5+.5) + (5.5+.5) + (2.5+.5) + (.5+.5)   = 22

We both mistook how many loaves were after the third customer

So 15 is the only workable answer I can come up with, which is appropriate because 1, 2, 4, 8 is a term that is a successive powers with a power of two (or 2x8-1=goal)

[ed]

word up. nice catch doc! too fast!

d. 23 to start with: 1st customer takes 11.5+.5 leaving 11, 2nd takes 5.5 +.5 leaving 5, 3rd takes 2.5 +.5 leaving 1, 4th takes .5 +.5.

that decidedly does NOT compute. nice work, superpokenerd.

[joae1975]

I pm'd you.  Are there multiple answers for the last question?  Becuase I got 15 and ed got 23 and both seem to work.  Ed, I'm curious as to how you solved the 4th.  What i did was i defined N to be the number of loaves to start with and then algebraically determined that each person must take (N+1)/2 , (N+1)/4, (N+1)/8, and (N+1)/16 loaves respectively.  Based on my solution, it seems that any number N such that the prime factorization of N+1 involves 16 (2^4) would serve as a viable answer.  In my solution 23 doesn't appear as a viable solution but evidently it works, i'm just curious how you got it.

1. Bob is blind
2. 6
3. 49
4. 15

I had to post your PM to show that you were indeed the first person to come up with all four correct answers.  Wow!  that was fast.  I should have picked harder ones!   Nice job!!  And yeah, 23 doesn't work because that would leave 0.5 loaves left.  I think the question should have mentioned that all of the bread would be gone.  I copied it from a book, didn't think of that, but in any case, that's the luck of the draw.

Congratulations SuperPokernerd, you truly live up to your name, haha!  So, my next question, what yoyo's are you looking for?

[SuperPokenerd]

Yay  Math has never failed me yet .  Alright, I will be messaging you soon with what yoyos I like.  Thanks again and merry christmas.

EDIT:  Just pm'd you my yoyo preferences and address.  Oh, and if you could, don't tell me what you're sending me.  I want it to be a surprise.