[Interjection sequence]

On 4/30/2019 at 2:26 AM, Thalia said:

You figured it "ou"?  Lol. Just caught on to Captain Ed's hint. Was wondering why that wording was nagging at me... If you didn't get it, I was going to recommend listening to the song Message in a Bottle. That ending aught to do it. 

 

... and as the title of one of ABBA's songs too!

[Crazy sequence]

Perhaps you've seen this one before, but I've added an extra twist to it!

 

    What are the next two entries in this sequence?

 

All credit due to the original designer from whom I've borrowed it (source to be disclosed once question is answered).

[April Semi-Quickie]

Thalia ...

Spoiler

1.4142  is also the 4th root of 4.  Now you ought to get it!

 

[Mr]

 

Spoiler

1st hr: travel = 2/5 (0.4); distance left = 1 - 2/5  = 3/5 (0.6)

2nd hr: travel = 1/3 * 3/5 = 3/15 = 1/5 (0.2); left = 3/5 - 1/5 = 2/5 (0.4)

3rd hr: travel = 1/4 * 2/5 = 2/20 (0.1); left = 2/5 - 2/20 = 4/10 - 1/10 = 3/10 ( 0.3)

4th hr: travel = 1/2 * 3/10 = 3/20 (0.15); left = 3/10 - 3/20 = 6/20 - 3/20 = 3/20  (0.15)

Remaining distance to travel = 0.15 = 20 miles

Total distance traveled = 100 - 0.15 = 0.85 = 20 * 0.85/0.15 = 113⅓ miles

 

[April Semi-Quickie]

Nobody wants to know why?

[Find the missing value]

More ideas ...

Spoiler

 

[Interjection sequence]

Both Captain Ed and Thalia have transmitted vital clues in their previous remarks. Eish man, now you ought to get it!

[Find the missing value]

... this ... (not thus)!

[Interjection sequence]

Flamebirde, you're going to kick yourself!

[Find the missing value]

The way I see it.

Spoiler

[Find the missing value]

I know, but somebody will perhaps!

Spoiler

Used trial and error up to 50 000. Don't know how to prove it mathematically (yet). I believe the statement will only be true at infinity.

[Interjection sequence]

On 4/24/2019 at 7:59 AM, CaptainEd said:

Another derailed train of thought:

 

  Hide contents

 

Equilateral, Isosceles, Scalene, Hyperbolic(?), 5-dimensional (???)

 

 

I like this fresh approach Ed, but there is actually a very, very simple explanation!

 

14 hours ago, flamebirde said:

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something to do with unicode maybe? it can't have to do with the order of the letters of the alphabet... I have a feeling my mind is too burnt out on organic chemistry to puzzle this one out.

 

Not the order, correct.

4 hours ago, Thalia said:

Seems pretty obscure. Gave up and found it using Google. But on the other hand, 

 

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You may have just inspired me to learn more of the "language" beyond S and O. So thanks for that.

I can clearly see that you've got it!

[Find the missing value]

Spoiler

For 11 up to 9999 it's a lie! After that, maybe too.

Some figures get close, however, e.g. 25, 37, 449, 4499, one or two off the mark..

 

[Find the missing value]

Spoiler

Answer withdrawn

 

[April Semi-Quickie]

Spoiler

1.4422, 1.4142, 1.3797, 1.3480, 1.3205, 1.2968, 1.2765, 1.2589, ...

Answer = 4422, 4142, 3797, 3480, 3205, 2968, 2765, 2589, ...

 

 

[Interjection sequence]

Spoiler

 

In the first instance (E I S H 5), 4 letters plus one numeral occur in the sequence. No pronunciation involved.

In the second case (T M O CH 0), "CH" is not a pronunciation, but merely a representation of the digraph "ch". Three  letters, one digraph and one numeral involved.

 

I called the original OP an interjection sequence since the word "eish" (pronounced "aysh") incidentally appears in the sequence. It has nothing to do with the solution, however! You can google its meaning.

 

 

[Easy Root]

Spoiler

Indeed a very easy one! I was first thinking of having one find x and y in:

"xth root of x = yth root of y" [or x^(1/x) = y^(1/y)]

If x<>y, then only one solution:

x = 2 and y = 4

 

[Easy Root]

Find x in:

 

 

[Bringing back an old one.... Making Toast]

On 4/18/2019 at 12:39 AM, Pirate8 said:

 

Left	side		Right	side
1-5	A1 in		6-10	B1 in
6-35	A1 toast		11-40	B1 toast
36-38	A flip		41-45	B out
39-68	A2 toast		46-50	C in
69-74	A out		51-80	C1 Toast
75-79	B2 in		81-83	C flip
80-109	B2 toast		84-113	C2 toast
110-114	B out		114-116	C out
Manual operations must not overlap.

Shouldn't the last entry (for C out) read 114-118?

[Interjection sequence]

 

That's one possibility!

 

Spoiler

Depending on language:

CH (Scottish/German ”ch”), Χ (Greek chi/Russian xa), Ĥ (Esperanto), phonetic χ

or

Š (Croatian), phonetic ʃ

 

[A special Factorial relationship]

Spoiler

NOOOO!

(1/2)! * (1/2)! = sqrt(pi)/2,

but (-1/2)! * (-1/2)! = pi

 

[A special Factorial relationship]

Spoiler

(1/2)! = sqrt(pi)/2

(-1/2)! = -sqrt(pi)/2

(-1/2)!*(-1/2)! = {-sqrt(pi)/2}^2 = pi/4 ~ 0.7854 (?)

 

 

[Interjection sequence]

Plainglazed ...

Spoiler

5 is correct.

Answer the second sequence too and then we can reveal the reasons why.

2nd one a bit trickier, isn't it?

 

[Bringing back an old one.... Making Toast]

Spoiler

116 seconds (or possibly even 106 seconds) presuming first two pieces are already in place.

Toasting alone takes 90 seconds for slices numbered 1, 2 and 3 with sides A and B.

Stages: (1) 1A  and 2A under grill (30 sec), followed by (2) 1B and 3A under grill (30 sec); finally (3) 2B and 3B under grill (30 seconds)

Normal additional time for single movements:

End of 1st stage: Slice 1 flipped from 1A to 1B (3 sec), 2A removed (5 sec), 3A inserted (5 sec)

End of 2nd stage: Slice 1 removed (5 sec.), slice 3 flipped from 3A to 3B (3 sec), slice 2 (2B) re-inserted with flip side up (5 sec)

End of 3rd stage: Done

Normal additional time = 26 seconds

Total time = 116 seconds.(1:56)

Exchange in one go:

If one is allowed to do simultaneous movements (exchanging in one switch of 5 sec), 10 seconds can be deducted, i.e. a total time of 106 seconds (1:46)

 

 

[Fair division of sausages]

Spoiler

Thalia, was your 42 a typo for 24 or the total of 24+18?