The worlds first riddle!

Mark:



BUSINESS EARNINGS
$333,062,500 $


To begin with, you want to know the total number of days: 365 x 50 = 18250. By experimentation, the following formula can be discovered, & used to determine the amount earned for any particular day: 1 + 2(x-1), with x being the number of the day. The title again holds a hint, although this 1 may have been a bit more obscure. Take half of the 18250 days, & pair them up with the other half in the following way: day 1 with day 18250, day 2 with day 18249, & so on, & you will see that if you add these pairs together, they always equal $36500. Multiply this number by the total number of pairs (9125), & you have the amount you would have earned in 50 years.




GRANDMASTERS
chess nuts boasting in an open foyer.

The search for the unknown can never be so described. :wink:


TRUE STORY
on a chess board
horse = knight
tower = rook
priest = bishop

DISCS
9

Let the total number of black discs in the box be b and the number of white discs be w.
Clearly if b=w, the player would win every time; and for this problem we are given that b>w.

We shall express a win by the use of strings; for example, the sequence:
W, WW, WWB, WWBW, WWBWB, WWBWBB produces the winning string, WWBWBB, that contains three of each colour.

For each winning string, it will only contain an equal number of black and white discs for the first time when the final disc in the string is taken. For example, WBBW does not represent a valid winning string, as it contained an equal number of black and white discs after the second disc was taken. Therefore, given a winning string, we can safely invert the string to obtain a different winning string. For example, WWBWBB and BBWBWW are dual winning strings. Hence there are an equal number of winning strings that start with B and W.

As there are more black discs than white discs, any string starting with W must be a winning string; there will always be enough B's to eventually match the number of W's before the final disc in the box is taken.
P(1st disc W) = w/(b+w), hence P(winning) = 2w/(b+w), where b≥w.

Therefore solving 2w/(b+w) = 1/2, leads to b = 3w.
As b+w = 3w+w = 4w = 12 ⇒ w = 3. Hence there are 3 white discs and 9 black discs in the box.

Mark wrote, "(assuming I've answered correctly)"

Yeah, right. :wink:


DP wrote, "A white horse jumped over a tower...... I shall leave this one for nickthegoon." :wink:

Well the guy said he was a chessnut!




If seven female web programmers can format 1001 puzzles in 429 minutes, how long does it take three male web programmers to format those 1001 puzzles



In training for a competition, DP finds that swimming downstream (with the current) in a crock infested river he can swim 2 miles in 40 minutes, and upstream (against the current), he can swim 2 miles in 60 minutes.

How long would it take him to swim a mile in still water


Happy New Year to you ALL, have a good one.

Mark,

Iraq

Yikes! You've got bigger worries than reading my posts...

Maybe overly simplistic???
Puzzles
986 minutes
wherre there are 2.3 times more females than males working. the time for the males will be increased by 2.3 or 429 * 2.3 = 986.

WEB PROGRAMMERS
Assuming gender is irrelevant, 1001 minutes.

DP SWIMMING
24 minutes

Happy New Year to you, too. We're getting doused with rain right now.

Note the larger font. It should be readable just by highlighting.

The method is correct, but you shouldn't round.

Thanks

swimming 25 minutes

50 minute average to swim up and down stream for 2 miles. 1/2 that for 1 mile = 25 minutes.

I see what you mean.


Try does come up with some fun things

Bejeepers Ralph, you don't programme nuke's do you?

A word to the wise; Watch your six around here. Only I and Bill O'Reilly know there are more card carrying, tree hugging UCLA members than you could shake a stick at around here. Oh man, I do love the smell of napalm in the morning. (Second chorus, the same as the first)

"Try does come up with some fun things"

What's your game? Are you out to ruin me? Come back - 10-4.



What the heck Ralph, have 100 credits on the house.




If we consider 2-digit numbers, there are exactly 18 numbers that contain the digit one:

10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
21, 31, 41, 51, 61, 71, 81, 91

True or False

As there are ninety 2-digit numbers, the probability of a 2-digit number containing a one is 18/90 = 1/5




What proportion of 3-digit numbers contain the digit one

Numbers:
Part A is true
part B is correct
Part C 1/1 and 1:4.7

sorry
Part c 1:2.5

A water supply depot is located next to a desert. The crew have 3000 bottles of water that have to be transported to the front line by camel, across a 1000 kilometre stretch of desert.

The crew have only one camel, which carries a maximum of 1000 bottles at any moment in time, and drinks one bottle every kilometre it travels.

What is the largest number of bottles that can be delivered to the troops

THREE DIGIT NUMBERS
244/900 = 61/225 = .271111...

Oh! My freeking head. Never, never ever, until the next time. Strange that after all the fireworks the old place looks just the same as last year.

Talking of years, we enter the forth year. How many problems remain unsolved?

May I also take this opportunity to finally put to rest the rumour that a2k pay me $100.000 pa. Lemme tell ya, I wouldn't get outta bed for that!



Mark:

WEB PROGRAMMERS
Assuming gender is irrelevant, 1001 minutes.
(Probably not if you want baby programmers)

The total amount of work is 7 times 429 programmer-minutes, so 3003 programmer-minutes. So 3 programmers will need 3003/3 = 1001 minutes.



DP SWIMMING
24 minutes


You are able to swim downstream at 3 miles an hour, & upstream at 2 miles an hour. There is a difference of 1 mile an hour, which is the river helping you in 1 direction, & slowing you in the other direction. Average the 2 rates, & you have the rate that you can swim in still water, which is 2.5 miles an hour. You can thus swim a mile in still water in 24 minutes.


THREE DIGIT NUMBERS

Unless there is a serious challenge, shall for evermore be known thus:


There are three mutually exclusive cases for consideration:
1**, (1')1*, and (1')(1')1.

First Digit Second Digit Third Digit Combinations
1 0-9 0-9 1×10×10 = 100
2-9 1 0-9 8×1×10 = 80
2-9 2-9 + 0 1 8×9×1 = 72
Total 252

There are 9×10×10 = 900 numbers that contain three digits.

Hence the proportion of 3-digit numbers containing the digit one is 252/900 = 7/25.




A military column of 1 km length marches with a constant speed of 6 kilometers per hour.

A courier from the back of the column is sent to the head of the column by bike to deliver a message.

Arriving at the front, he instantly returns. Upon his return, the back of the column has travelled a distance of 1 km since the start of his errand. The courier drove with constant speed.

How fast did the courier bike



Working from left to right in a number, if the next digit is greater in value than the preceding digit, we say that the digits are strictly increasing: 15689, 35679, and 13478 are examples of 5-digit numbers with this property.

Given a number has strictly increasing digits, what is the probability that it contains 5-digits


Gosh! Them guys in the forward O.P. sure are getting thirsty.

Water:
Max water than can be brought is 400 bottles.
whether it is done by 200 km legs or 100 km legs the amount comes out the same (unless I messed up somewhere.)

No, I'm telling ya, the last time I saw an answer like that, the dude came from Louisiana. I kid you not, our boy's need that water.

Which reminds me:

A Louisiana man walks into a travel agancy in response to an ad about free river cruises. As the man described why he was there to the lady behind the desk, the woman hit a button, two men spring up behind the guy, beat him up, take his wallet , stuff him into a sack, and throw him out back into the river.

A few moments later another Louisiana man walks in and also begins to speak when the woman hits the same button. The two men spring out, beat him up, stuff him in a sack, steal his wallet, and throw him out back into the river.

A few miles down river the two men catch up to one another and the first man says, "I wonder if they serve dinner on this cruise?"

The second replies, "They didn't last year."


Now, where's me banjo?

THREE DIGIT NUMBERS
I know where I went wrong. I figured 100 + 8*18 (18 from the 2-digit answer). However, that excludes ?01 for ?=2 to 9. 244+8=252.

Oops.

The desert and courier problems are repeats, so I'll abstain.

[size=8]STRICTLY INCREASING
For N digits (0 < N < 10), there are C(9,N) numbers. Therefore, the total number of strictly increasing numbers is 2^9 - 1 because N can't be zero. So, the answer is C(9,5) / 511 = 126/511.[/size]

Good joke!

"I figured 100 + 8*18 (18 from the 2-digit answer)."

Who was it I ask, who confused things by putting a somewhat unnecessary answer before the question?

Yoo hoo, over here!

Please don't feel bad at having a 2006 record of zero, just join gunney.

Yo! I'm a badass, yus I am.



13! = 13 × 12 × 11 × ... × 2 × 1 = 6227020800.
It can be seen that 13! contains two trailing zeroes.

How many trailing zeroes does 1000! contain

[size=8]1000!
1000/5 + 1000/25 + 1000/125 = 200 + 40 + 8 = 248[/size]