The worlds first riddle!

[size=7]PRIME TIME
2-2 = 0

ELEMENTARY
c[/size]

This is the question: What is the next number in the series.

5 6 7 8 8 8 8 8 ?

Due in part to an abundance of good will, I give you:
The answer is 9.

For those at the cutting edge of genius, can you explain why

What came before the 5?

Was it:
1 1 2 2 3 4 4 4
a(1) = a(2) = 1; thereafter a(2n+1) = a(n+1) + a(n), a(2n) = 2a(n)

Appears to coincide with following sequence: Let n >= 1. Start with a bag B containing n 1's. At each step, replace the two least elements x and y in B with the single element x+y. Repeat until B contains 2 or fewer elements. Let a(n) be the largest element remaining in B at this point.

or:
1 1 1 2 2 3 3 3 4 5 5 5
Number of numbers <= n with an even number of prime factors (counted with multiplicity).

or:
2 2 3 4 4 4
Survivor number for 2nd-order Josephus problem.

or:
1 2 2 3 4 4 4
Size of the largest subset S of {1,2,3,...,n} with the property that if i and j are distinct elements of S then i XOR j is not in S, where XOR is the bitwise exclusive-OR operator.

or:
1 1 2 2 2 3 4 4 4 4 5
a[n] =a[a[n-1]] + a[n -1- a[n-1]]

or something else?

Here's one to ponder as you're relieving yourself at the ballgame after several brews:

1 2 4 8 16 36 136

10 (or is that the "addstract" answer you aren't looking for?)

Mark, I thought your sequence looked remarkably easy - I need glasses. Don't give anything away, I am still on the case.

BTW : 10 I aren't looking for any udder.

Whilst working on permutations I stumbled upon the following unique set.

3-15-19-22-23-

On reflection, that might be as easy as abc.

3-15-19-22-23-?
???

Mark, I thought I had the answer to your series with the score on a dartboard (of all things) however, I cannot see a pattern. That said, amongst all my notes the number 141 appears most of all.

If, "one to ponder as you're relieving yourself at the ballgame after several brews" is a clue, then, sadly it has passed me by. Unless it is Yd/Rush 3.8

Moving swiftly on:

3-15-19-22-23-(24)(26)
c - o -s -v -w - x - z
C -O- S- V- W -X - Z
They are the only letters that are identical in both upper and lower case.

If you have a sixth sense, it may help you to solve this puzzle:

6 396 2376 1425.6 8.5536

1,2,4,8,16,36,136,216,672,2592,10656,35904,167808,426240,...

Given a row of n urinals, all initially unused, how many ways are there for n men to choose the urinals, assuming each always chooses one of the most distant urinals from those in use already?

SIXTH SENSE
513216 with a decimal point somewhere.

My dear Mark, I do apologise for my propensity to be on the s l o w side. However, tie me to a hog and call her Elli May. I cannot see the series. Perhaps you would be so kind as to elucidate.

"1,2,4,8,16,36,136,216,672,2592,10656,35904,167808,426240,... "

Furthermore, is, "Given a row of n urinals, all initially unused, how many ways are there for n men to choose the urinals, assuming each always chooses one of the most distant urinals from those in use already?" a new puzzle? Alternatively, is it a further clue to the above? I only ask because of this attraction with public toilets is quite worrying.


Mark:
SIXTH SENSE
513216 with a decimal point somewhere.

6 396 2376 1425.6 8.5536 ?

.00513216. Multiply the first number, 6, by 66, which yields 396; multiply 396 by 6, & then multiply the product of this by .06, & the product of that by .006.


No, I'm serious, I've had it with series - never again. Unless…


A worker earns a 5% raise. A year later, the worker receives a 2.5% cut in pay, & now her salary is $22702.68. What was her salary to begin with



Two trains, each two miles long, enter two one mile long tunnels that are two miles apart from one another on the same track. The trains enter the tunnels at exactly the same time. The first train is going 5 miles/hour, and the second train is going 10 miles/hour.

What is the sum of the lengths of the two trains that will protrude from the tunnels at the exact moment that they collide; assuming that neither train changes its speed prior to collision

The trains are on the same track headed in opposite directions (i.e. directly toward one another).

The sequence is the answer to the urinal question.

[size=7]WORKER
$22,176

TRAINS
The rear 2/3 mile of the slower train will not yet have entered the tunnel. The rear of the faster train will be 2/3 mile into the tunnel. The two miles of track between the tunnels will be occupied by the trains. All told, 2 2/3 miles worth of trains is exposed.[/size]

Mark:

Message received. :wink:

WORKER
$22,176

TRAINS
The rear 2/3 mile of the slower train will not yet have entered the tunnel. The rear of the faster train will be 2/3 mile into the tunnel. The two miles of track between the tunnels will be occupied by the trains. All told, 2 2/3 miles worth of trains is exposed. /


I am know right ing a book to lern you all beter engliss;

Two numbers are given in each sentence that need to be replaced by words. Each word is an anagram of the other - each word can be formed by rearranging the letters in the other word.
The numbers given in each sentence indicate the number of letters in each word - Comprendo!


Gus had driven in his tractor over a (4) to find a restaurant that served (4) pie.



Don't stop now Set, if you read further you will see that he (4) on the (4) of March.

[size=7]COMPRENDO
mile (key) lime

dies ides[/size]

I love fruit, especially (6) and sour (6)!


The raised (4) (4) listeners by making it possible for the crowd to see the speaker.

[size=7]melons lemons
dais aids[/size]

Mark:

COMPRENDO
mile (key) lime

(Key)! Say what? - Alamos lime pie. Now, you are talking.
I like this pie because it does not have to be baked.

However, if you want to get flour and dirty, try:

Lime Pie

For two pies, make pie crust, separate into two batches, roll and place in two pie tins. Poke holes in the bottom of the pie crusts and bake until slightly brown, approximately 10-12 minutes in 350' oven. Cool.

Separate 6 eggs placing the yolks in one bowl and the whites in another, preferably copper. (Whites whip better in a copper bowl). Be absolutely certain that you do not get any of the yolk or any trace of oil in the bowl which contains the egg whites.

Whisk yolks until light yellow in color and add to the yolk mixture, one can at a time:

3 cans Eagle Brand condensed milk, whisking well after each one
To this mixture, whisking after each addition, add in 3 parts:
1 ½ scant cups fresh lime juice and zest of 3 limes.
In the copper mixing bowl add a dash of salt, or a tiny pinch of cream of tartar, to egg whites and beat until stiff but not dry.
Fold egg white mixture into egg yolk mixture using slow smooth strokes which blend the whites in without breaking them down.

Do not over mix. When mixture is blended, pour into baked pie crusts.
Bake at 350' for 10 Min. Cool.

The egg whites can also be treated as a Meringue and baked at 475' on top of the pie for a couple minutes, until lightly browned.

Serve topped with whipped cream.


dies ides
melons lemons
dais aids



It is amazing how Joe (4) his (4) through his opponent's guard to land a punch.



Chai's face became (4) when she thought that try was going to (4) from the balcony.

[size=7]fits fist
pale leap[/size]

Are these so difficult, that only one man in the whole world can answer give?

Well - I guess so. The $64,000 questions.


What a (4) life the gangster rap did (4).



Francis used a special (4) to break into the safe and make off with the (4).