[Two Rectangles]

There are MANY(at least 51) that meet these criteria...here are all 51 with side lengths under 1000...10x87 1x29011x48 1x17612x35 1x14015x22 1x11020x174 2x58021x122 2x42722x96 2x35224x70 2x28026x57 2x24730x44 2x22030x261 3x87031x42 2x21733x144 3x52836x105 3x42040x81 3x36042x244 4x85444x192 4x70445x66 3x33048x140 4x56049x132 4x53952x114 4x49453x54 3x31855x240 5x88058x195 5x75460x88 4x44060x175 5x70062x84 4x43468x75 4x42570x123 5x57471x120 5x56872x210 6x84075x110 5x55078x171 6x74180x162 6x72081x158 6x71184x95 5x53284x245 7x98089x210 7x89090x132 6x66093x126 6x651102x161 7x782104x228 8x988105x154 7x770106x108 6x636111x200 8x925112x141 7x752120x176 8x880124x168 8x868135x198 9x990136x150 8x850159x162 9x954...

Nice.

Curious about your algorithm.

Mine ran forever with n=100, (and came up empty.)

I tried direct solutions also, restricting the first to be square and the second to be 1xm.

Came up empty again.

It's unbelievably inefficient and very brute force, but it worked like a charm:

public class Dummy {
   public static void main(String... args) {
      for (int a = 1; a < 1000; a++) {
         for (int b = a; b < 1000; b++) {
            for (int c = 1; c < 1000; c++) {
               for (int d = c; d < 1000; d++) {
                  if ((a * b) == 3*(c * d) && 3 * (2 * a + 2 * b) == (2 * c + 2 * d)) {
                     System.out.println(a + "x" + b + "   " + c + "x" + d);
                  }
               }
            }
         }
      }
   }
} 

[Two Rectangles]

There are MANY(at least 51) that meet these criteria...here are all 51 with side lengths under 1000...

10x87 1x290

11x48 1x176

12x35 1x140

15x22 1x110

20x174 2x580

21x122 2x427

22x96 2x352

24x70 2x280

26x57 2x247

30x44 2x220

30x261 3x870

31x42 2x217

33x144 3x528

36x105 3x420

40x81 3x360

42x244 4x854

44x192 4x704

45x66 3x330

48x140 4x560

49x132 4x539

52x114 4x494

53x54 3x318

55x240 5x880

58x195 5x754

60x88 4x440

60x175 5x700

62x84 4x434

68x75 4x425

70x123 5x574

71x120 5x568

72x210 6x840

75x110 5x550

78x171 6x741

80x162 6x720

81x158 6x711

84x95 5x532

84x245 7x980

89x210 7x890

90x132 6x660

93x126 6x651

102x161 7x782

104x228 8x988

105x154 7x770

106x108 6x636

111x200 8x925

112x141 7x752

120x176 8x880

124x168 8x868

135x198 9x990

136x150 8x850

159x162 9x954

...

[Making it whole]

5/34 + 7/68 + 9/12 = 1.0

[Lines for Squares]

Probably not the optimal for all of them, just the first pass numbers I got...

1: 4
2: 5
3: 6
4: 7
5: 6
6: 7
7: 8
8: 7
9: 8
10: 9
11: 8
12: 9
13: 10
14: 8
15: 9

[Activity courses]

I found 2 solutions...Basically I got it down to this:

Monday 6-8: Judo - Linda
Monday 8-10: Volleyball - Jane
Tuesday 6-8: Balance - Linda
Tuesday 8-10: Squash - Pete
Wednesday 6-8: Ballet OR Tumlbling - Jane
Wednesday 8-10: Tumbling OR Ballet - Bob
Thursday 6-8: Karate - Bob
Thursday 8-10: Floor - Rick
Friday 6-8: Handball - Pete
Friday 8-10: Table Tennis - Rick

From what I can tell, both solutions work to satisfy all of the clues/requirements...the ONLY part I'm a little confused about that would completely screw up my approach is clue 6:
6. Pete has one course the same night as the balance-beam class is held and his other course later the same evening as one of Rick's courses.
Does that mean "later in the same evening" which would then imply it would be during the 8-10 slot...or does it mean "later in the week the same evening"? I took it to mean the latter...which is why I have Pete from 6-8 on Friday and Rick from 8-10...if you meant the former, then my solution does not work...

[How Low can U go?]

Alright, I realized my mistake...here ya go:

a = 0.39
b = 5.2
c = 9

Gives you a 3 digit number of 100, but a min value of 6.854009595613435

Nice puzzle!

[How Low can U go?]

...assuming a doesn't equal 0 (since that would mean it isn't truly a three digit number) I'd be curious to see a smaller value of M / (a + b + c)

I'm going to stick by 199/19 = 10.473684210...

[How Low can U go?]

a = 1, b = 9, c = 9 for a minimum value of 10.473684210526315

[At the Snack Shack]

...on how the cash register deals with rounding...if it follows the "standard" round-half-up method, then I see 39 solutions:

1.06, 2.23, 2.41
1.06, 2.24, 2.40
1.06, 2.25, 2.39
1.06, 2.26, 2.38
1.06, 2.27, 2.37
1.06, 2.28, 2.36
1.06, 2.29, 2.35
1.06, 2.30, 2.34
1.07, 2.13, 2.50
1.07, 2.14, 2.49
1.08, 2.06, 2.56
1.08, 2.07, 2.55
1.09, 2.01, 2.60
1.09, 2.02, 2.59
1.10, 1.97, 2.63
1.11, 1.93, 2.66
1.12, 1.90, 2.68
1.13, 1.86, 2.71
1.14, 1.83, 2.73
1.15, 1.81, 2.74
1.16, 1.78, 2.76
1.17, 1.76, 2.77
1.18, 1.73, 2.79
1.19, 1.71, 2.80
1.20, 1.69, 2.81
1.21, 1.67, 2.82
1.22, 1.65, 2.83
1.24, 1.62, 2.84
1.25, 1.60, 2.85
1.27, 1.57, 2.86
1.29, 1.54, 2.87
1.31, 1.51, 2.88
1.32, 1.50, 2.88
1.35, 1.46, 2.89
1.36, 1.45, 2.89
1.37, 1.44, 2.89
1.38, 1.43, 2.89
1.39, 1.42, 2.89
1.40, 1.41, 2.89

[An ungrateful award]

150 2/3 yards + 45 yards 3 inches = 195 3/4 yards exactly...which means the plot of land is a straight line...not much land at all...I'd be pretty upset as well.

[What am I?]

The letter "r"

[A miraculous voyage]

But, how can it be a tetrahedron? The cities are just 5 miles away. Any 4 points on the surface of the earth which are also the vertices of a tetrahedron must be at a distance of 1.63 times the radius of the earth (which is about 6500 miles!!!).

...I'd say he could have visited an asteroid or some other EXTREMELY small body in space to accommodate the shorter distances between towns...The OP doesn't say he was on Earth while doing this trip...

Plus, it truly would be a "miraculous voyage": travel to a small asteroid, land on it safely, find that there are indeed 4 "towns" set up by someone, visit them all, and return back to Earth safely. And never in my life, at least, would I ever expect to see such a thing happen...

So I'll go with that as my answer.

[Word Puzzles/Riddles(?)]

Ah...see, I read #4 to mean "is six letters long" not "contains six DISTINCT letters". Because, really, even if a letter repeats itself, it's still a letter...so only 6-letter words can "contain 6 letters".

HEATHEN technically contains 7 letters...it just it has 2 Es...

Either way...Good catch, ShadowAngel7...nice interpretation.

[Solve the cryptogram II]

21,8,10,24

You obviously know the answer, but your first letter is wrong...should be:

2,8,10,24

[Word Puzzles/Riddles(?)]

TWENTY NINE

Differently

That that is, is. That that is not, is not. Is not that it? It is.

Question: are you allowed to skip letters as long as you don't rearrange them? Because if not, I can come up with a word that has 6 words in it, but not 8:

herein - he, her, here, ere, rein, in

Unless you want to count "en" as a word, then I found 7:

hasten - ha, has, hast, haste, ten, as, en

If you are allowed to skip letters, then there are a number of words that work...including hasten which actually has 9 that I found

hasten - ha, has, hast, haste, hen, ate, hate, ten, as

[Word Puzzle]

W A P I T I
A C U M E N
P U P P E T
I M P U T E
T E E T E R
I N T E R N

The only one I wasn't really aware of was wapiti...but after getting the others and a simple google search for "apiti deer", it came up...who knew??

[Barcode - read and answer]

view #29...#29 of what? I guess that's the puzzle?

[Weighing problem again...]

but my first pass through to find both fakes, assuming that the balance scale simply tells you "heavier" or "lighter" and that you can't measure HOW MUCH heavier or lighter is 5 weighings...I have a couple different approaches using 5 weighings, but will look for fewer.

[An oldie a professor once told me on Area and Perimeter]

This is actually a duplicate puzzle as the one I posted a long while ago on these forums:

The only difference is the perimeter would obviously be twice the "SUM" in the problem I posted...but just divide by 2, and it's the same logic to figure out...I love this puzzle...

4 x 13

[Division of a Will]

Quick question: when you say "equal (or better than equal) percentage"...from whose perspective are we talking?

If we are saying that each PERSON believes they have AT LEAST equal percentage of the worth, then we first look at what each person believed the old man was worth:

ALBERT: $14,001,670...which means "equal" to him would be everyone getting $3,500,417.50...

ERIC: $14,601,730...which means "equal" to him would be everyone getting $3,650,432.50

THERESA: $13,501,335...which means "equal" to her would be everyone getting $3,375,333.75

SONYA: $16,002,050...which means "equal" to her would be everyone getting $4,000,512.50

If we use those, we can simply give Sonya the house and all of the belongings...and then divide the remaining $12,000,000 in cash evenly between the rest of the siblings.

To Sonya, she got more than an equal share ($4,002,050) and everyone else got $4,000,000...so she's happy

To Theresa, she and everyone else but Sonya got more than an equal share ($4,000,000) while Sonya only got $1,501,335...so she's happy

To Eric, he and everyone else but Sonya got more than an equal share ($4,000,000) while Sonya only got $2,601,730...so he's happy

To Albert, he and everyone else but Sonya got more than an equal share ($4,000,000) while Sonya only got $2,001,670...so he's happy

Doing this gives everyone the perception that they had a more than equal share of the total worth...

However, from the lawyer's perspective, he would see Sonya getting much less than equal, simply because the value of the house most likely is closer to the average ($2,275,000)...which means with this approach, Sonya would have much less than an equal share...

That's why I'm wondering from whose perspective we are defining "equal".

[Initial reactions - Lyrics]

But I figured AIK TIA IA IATL is " I know that I am I am I am"

The Luckiest:

I don't get many things right the first time

In fact, I am told that a lot

Now I know all the wrong turns

The stumbles and falls brought me here

And where was I before the day

That I first saw your lovely face?

Now I see it every day

And I know

That I am

I am

I am

The luckiest

Next door there's an old man who lived to his nineties

and one day passed away in his sleep,

and his wife, she stayed for a couple of days, and passed away

I'm sorry I know that's a strange way to tell you that I know we belong,

That I know

That I am,

I am,

I am,

the luckiest

[Shuffle to Double]

Just validated my above answer with a simple program...in case you're curious, here's the source:

public class SuffleDouble {
   public static void main(String[] args) {
      for (long i = 1; i < 1000000; i++) {
         permutation("", i + "", i);
      }
   }
 
   private static void permutation(String prefix, String str, long origVal) {
      int n = str.length();
      if (n == 0) {
         long newVal = Long.parseLong(prefix);
         if (origVal * 2 == newVal) {
            System.out.println(origVal + " * 2 = " + prefix);
            System.exit(0);
         }
      } else {
         for (int i = 0; i < n; i++) {
            permutation(prefix + str.charAt(i), str.substring(0, i) + str.substring(i+1, n), origVal);
         }
      }
   }
}

[Shuffle to Double]

125874...can be shuffled to be 251748

[Like Clockwork]

many gears spinning 'round,

numbers spill too unbound.

sapping energy of a spring,

adding adding everything.

whether weather is need to know,

or complex equations bust from flow.

memory, shift, register, digest;

come forth solution, progamming guest!

A CPU or motherboard...

[The coordinates]

https://maps.google.com/maps?q=58.76993413296066943466666666666667,5.62653852214286336&hl=en&ll=58.769853,5.626131&spn=0.002823,0.007693&sll=58.766667,5.616667&sspn=0.022586,0.061541&t=h&z=18&layer=c&cbll=58.769853,5.626131&panoid=8JxFaUdKATqfmIAZf_e55A&cbp=12,68.41,,0,0

There's your location. It's a house in Norway. I took the molecular weights of each compound and multiplied them together to get these coordinates:

N58 46.1960479

E5 37.5923113