The worlds first riddle!

VALLEY
137

You can always move down or to the right. Replace the letters with numbers that represent the number of paths down and to the right from that letter. Start by assigning 1 to the bottom and rightmost letters. Each of the others is the sum of the numbers immediately to the right and below. The final answer is the sum of the numbers on the left edge where the Vs were. It looks like this:

CHICKEN & EGG
Good joke!!!

CHANGE FOR A $50
I get 450

Francis, be assured you are on my good to know list.



Mark:
VALLEY
137

You can always move down or to the right. Replace the letters with numbers that represent the number of paths down and to the right from that letter. Start by assigning 1 to the bottom and rightmost letters. Each of the others is the sum of the numbers immediately to the right and below. The final answer is the sum of the numbers on the left edge where the Vs were.

What can I say; this was one of my best riddles. You are a one-guy answer factory.


Good joke!!!

Nice to see someone understood the punch line.


CHANGE FOR A $50
I get 450

That's strange, so do I. (ps7pm) :wink:




Determine the missing numbers in the following sequence of ordered pairs:


(1,3), (2,3), (3,5), (4,4), (5,4),
(6,3), (7,5), (8,_), (9,_), (10, _)



Find four distinct integers a,b,c,d such that
100 <= a,b,c,d <= 12000 and the sum of "all" the four of them
and the sum of "every" two of them are perfect squares.

(That is, a+b, a+c, a+d, b+c, b+d, c+d, and a+b+c+d are all
squares of integers.)


In this puzzle, you must turn MOOD into BARN by changing only one letter from the previous word.

M O O D
_ _ _ _
_ _ _ _
_ _ _ _

B A R N


Can you find the three missing words

ORDERED PAIRS
5, 4, 3 (an old one in disguise)

MOOD to BARN
moon - boon - born (these are fairly easy when the number of steps equals the number of letters that have to change)

Here's one to play with while waiting for the Super Bowl to start.

Determine the unique 9-digit integer M that has the following properties:
(1) its digits are all distinct and nonzero
(2) for every positive integer m = 2, 3, 4, ..., 9, the integer formed by the leftmost m digits of M is divisible by m.

For example if you had to do this with a 3-digit number, 123 would work because 12 is divisible by 2 and 123 is divisible by 3.

FOUR DISTINCT INTEGERS
386, 2114, 3970, 10430

That was a good one. It showed the worth of a spreadsheet!

Mark:

ORDERED PAIRS
5, 4, 3 (an old one in disguise)


The ordered pair is formed in the following manner:
(next integer, number of letters in the spelling of that integer)
e.g., eight has 5 letters in its name; hence, (8,5)


Well spotted, they are all ?'old' in one way or another.



MOOD to BARN
moon - boon - born (these are fairly easy when the number of steps equals the number of letters that have to change)


The easy ones are for ?'newbie's'



FOUR DISTINCT INTEGERS
386, 2114, 3970, 10430


These numbers satisfy the conditions below.

386+2114=2500=50^2
386+3970=4356=66^2
386+10430=10816=104^2
2114+3970=6084=78^2
2114+10430=12544=112^2
3970+10430=14400=120^2
386+2114+3970+10430=16900=130^2

Sketch of a non-brute-force solution:
The sum of all four (a+b+c+d) is the square of the right-hand side of a Pythagorean triple in three different ways, so it has to be divisible by a handful of prime factors, each of which is 1 mod 4 (or else the prime 2). Since it cannot exceed sqrt(4*12000) < 220, there are not that many candidates. The right one turns out to be 130=2*5*13.



Mark does it again

"Here's one to play with while waiting for the Super Bowl to start."


It started, finished, the night came and went. Morning brought a answer.

Therefore, M = 381654729.

Phew, who won the game?




Super Bowl riddle:

Can you match all 11 NAMES and POSITIONS of the Football team from the clues below


Lindon has scored more than the center; and surprisingly, Lowe has scored more than the right end.

Brown is heavier than the ends, guards, and center, but slower than the right half.

The fullback and center have wives and children.

The left half will marry Brown's sister, while the right half is also engaged.

Wilson stays with the left guard and his wife.

Frantz and Isherwood play a right or center position.

Isherwood punts better than the right half back.

Haston's and Lindon's wives are lawyers.

The right guard, right end, Wilson, Frantz, and Isherwood are all 5 bachelors.

The captain is also the quarterback.

The left tackle and Shickle often go fishing together.

Pleacher, Leonard, and the halves play cards with Wilson.

The tackles often play tennis with Haston and the quarterback.

The quarterback is getting a divorce. Brown was married before the quarterback or

left tackle, who was married last week.

Leonard and assistant captain Carpenter are not guards, ends or center.

The captain constantly relies on the linemen and Shickle.



Chad and Amanda are eating lunch when they are joined by Mike. Amanda has 5 sandwiches, Chad has 3 sandwiches, and Mike has none. They all share equally in the meal. I

f Mike pays $4.00 for what he ate, how should the money be divided between Amanda and Chad

Try: "Therefore, M = 381654729"
Right on!

CHAD & AMANDA
Chad: $0.50
Amanda: $3.50

Apologies:

Mark, you posted:
"A man set out at noon to walk from Appleminster to Boneyham, and a friend of his started at 1:20 P.M. on the same day to walk from Boneyham to Appleminster. They met on the road at 2:24 P.M., and each man reached his destination at exactly the same time. Can you say at what time they both arrived?"

I had the answer for:
A man set out at noon to walk from Appleminster to Boneyham, and a friend of his started at two P.M. on the same day to walk from Boneyham to Appleminster. They met on the road at five minutes past four o'clock, and each man reached his destination at exactly the same time. Can you say at what time they both arrived?

Woops, yes you were right. How was I to know there was so much going on in a place like ?'Appleminster'?


Mark:
CHAD & AMANDA
Chad: $0.50
Amanda: $3.50




Which year in our recorded history has had the greatest number of Roman Numerals in it

And which year will it be when this record is surpassed




Last summer, there was increased interest in the Powerball lottery when the jackpot offered $295 million. A group of machinists calling themselves "The Lucky 13" won the jackpot and took a cash payout of $161.5 million, with each receiving $8,944,447 after taxes.

Their winning numbers were 8-39-43-45-49 and powerball 13.
Powerball was first introduced in 1987 and the odds of winning were 1 in 55 million.

Five white balls were picked from balls numbered from 1 to 45 and one powerball was picked from another set of balls numbered from 1 to 45.

In November 1997, officials raised the odds of winning to one in 80 million, thus making likely jackpots of at least 100 million dollars twice a year.

Now five white balls are chosen from those numbered from 1 to 49, and the powerball is chosen from another set numbered from 1 to 42.

Suppose you want to lower the odds of winning Powerball to one in 300,000. What should the range of the white balls be and what should the range of the powerball be

(The maximum number of white balls that you may use is 50 and the maximum number for the Powerball is 50).

1888
2888

LOTTERY
18 white balls and 35 powerballs gets you as close as possible to 300,000.

The number N consists of 1999 digits such that if each pair of consecutive digits in N
were viewed as a two-digit number, then that number would either be a multiple of 17 or a
multiple of 23. The sum of the digits of N is 9599. Determine the rightmost ten digits of N.

DrewDad: (Good to see you around)

1888
2888


In 1888, there were 13 characters:
MDCCCLXXXVIII

In 2888, there will be 14 characters:
MMDCCCLXXXVIII


Mark:
LOTTERY
18 white balls and 35 powerballs gets you as close as possible to 300,000.


The odds are calculated by computing the combination of the white balls taken 5 at a time, and then multiplying by the number of balls from which the Powerball is chosen.

For example, the odds for the original Powerball is figured in the following manner:
45 C 5 * 45 = 54,979,155
Likewise, the current Powerball odds:
49 C 5 * 42 = 80,089,128

After examining all combinations of balls up to 50, only one solution gives us odds of one in 300,000:
Use white balls numbered from 1 to 18, and choose the Powerball from balls numbered 1 to 35.
18 C 5 * 35 = 299,880

The next closest values are:
19 White balls, 26 for powerball: 19 C 5 * 26 = 302,328
24 White balls, 7 for powerball: 24 C 5 * 7 = 297,528
23 White balls, 9 for powerball: 23 C 5 * 9 = 302,841




Seven guests at a restaurant came,

The first every day,
The second every other day,
The third every third day,
and so on to the seventh who came once a week.


When will they all come to dine at the restaurant on the same day
(I.e. what is the smallest number of days?)


What is the lowest integral values for A, B, C, and D where:

A + B = C
A + D = B
2C = 3D
B > 0



Mark, your question, "…The sum of the digits of N is 9599. Determine the rightmost ten digits of N."

Will take some MIT processing power, I will call back later.

RESTAURANT:
7 * 4 * 3 * 1= 84 days till the next they're all there

INTEGRALS:
A=1
B=5
C=6
D=4

I wrote it down on a piece of paper to calculate, but can't really read it anymore.. lol

RESTAURANT
420 days (Liessa forgot 5)

INTEGRALS
same as Liessa

Liessa:

INTEGRALS:
A=1
B=5
C=6
D=4

Mark:" same as Liessa"

Mark, if you have the same ?'integral's as Liessa, you must be one good looking babe.



Liessa:

RESTAURANT:
7 * 4 * 3 * 1= 84 days till the next they're all there.


Liessa, a warm welcome to this frayed thread. It would appear Mark is closer to the restaurant answer.



Mark:

RESTAURANT
420 days (Liessa forgot 5)




The least common multiple of 1, 2, 3, 4, 5, 6, and 7 is 420.



Whilst I ask ?'Hey Diddle Riddles' Mark (The Cruel) comes up with:

"The number N consists of 1999 digits such that if each pair of consecutive digits in N were viewed as a two-digit number, then that number would either be a multiple of 17 or a multiple of 23. The sum of the digits of N is 9599. Determine the rightmost ten digits of N."


Providentially, everybody knows that the answer is; 3469234685.

Apologies to those living along the Western seaboard when the power fell due to the computer power needed to formulate an answer. Blame cruel Mark.

BTW may I suggest you re-post them on the Math forum to test the response? They sure were mind boggling until you got an answer.





Hey Diddle Riddle:

A boy (Mark) and a girl (Liessa) ran a 100 meter race. The girl crossed the finish line when the boy had gone 95 meters, so she won the race by 5 meters.

When they raced a second time, the girl wanted to make the contest more even so she handicapped herself by starting 5 meters behind the start line.

If the two ran at the same constant speed as before, who won the second race
Explain (or give their times relative to each other).

My 14 year old daughter can beat me, so I don't feel bad about Liessa beating me.

Liessa will finish the race 0.25 meters ahead of Mark.

Try: "Providentially, everybody knows that the answer is; 3469234685."


Let N = 111...1222...2, where there are 1999 digits of 1 followed by 1999 digits of 2.
Express N as the product of four integers, each of them greater than 1.

lol! I'm no runner, but thanks.

Darn, I read the Restaurant thing wrong... I hadn't seen "and so on"