The worlds first riddle!

least # of balls --8
Wendy's right answer is 15
Jon pays $24

Rap

Try, how thoughtful of you to remark on my achievement of the 2000 post milesone. i couldn't have done it without threads such as this.

What number comes next in the pattern, and why
2, 3, 6, 15, 42, _____

123

2 + 3/3 = 3
3 + 3 = 6
6 + 3x3 = 15
15 + 3x3x3 = 42
42 + 3x3x3x3 = 123

i may have seen this elsewhere already, but i calculated it anew.

Neat yitwail

if F(0)=2 then
F(n)=F(n-1)+3^(n-1)

the sequence becomes
n f(n)
0 2
1 3
2 6
3 15
4 42
5 123
6 366
7 1095
8 3282
9 9843
10 29526
etal.

Rap

JON
$311

I am something people count on,
But I'm not your fingers or toes.
I am the comfort in your heart,
When your mind's not sure it knows.
People often call me blind,
For I have no eyes to see.
Several times I have been lost,
But I cannot be given away.

What am I

friendship, perhaps

Arithmetic error.

Jon pays $21 (I wrote a spreadsheet)

Jon owes $386 and gets $5 credit for every $25. So the first reduction is
Int(386/25)=15 Remander of 11 so he pays $(15*20+11)=$311

But under the rules this is greater than $25 and he gets a further reduction, and the second reduction is Int(311/25)=12 with a remainder of 11 so he pays $(12*20+11)=251

This is repeated until he finally owes less than $25. This takes 15 reductions and by my spreadsheet it figgered as

red/ amt/ n(386/25)/ rem/ n*20+rem
1 386 15 11 311
2 311 12 11 251
3 251 10 1 201
4 201 8 1 161
5 161 6 11 131
6 131 5 6 106
7 106 4 6 86
8 86 3 11 71
9 71 2 21 61
10 61 2 11 51
11 51 2 1 41
12 41 1 16 36
13 36 1 11 31
14 31 1 6 26
15 26 1 1 21

Finally after the 15 reduction the amount owed is less than $25

Rap

The folly of mistaking a paradox for a discovery, a metaphor for a proof is inborn in us.


Francis:
This can't make me weak, my name is Wallace...

(Adrian for Try)

Would that be William Wallace the Scots outlaw? You are more cryptic than Adrian. BTW have you seen him lately? I miss his quips.


Rap:

least # of balls --8 *
Wendy's right answer is 15
Jon pays $24


* I have 7 but do not have access to my notes. 8 does seem right though.


Yitwail wrote, "Try, how thoughtful of you to remark on my achievement of the 2000 post milesone. i couldn't have done it without threads such as this."

Don't blame me, that only accounts for about six. :wink:

I am something people count on,
But I'm not your fingers or toes.
I am the comfort in your heart,
When your mind's not sure it knows.
People often call me blind,
For I have no eyes to see.
Several times I have been lost,
But I cannot be given away.

What am I ?

friendship, perhaps
I like that answer. I have ?'Faith'

What number comes next in the pattern, and why
2, 3, 6, 15, 42, _____

123

2 + 3/3 = 3
3 + 3 = 6
6 + 3x3 = 15
15 + 3x3x3 = 42
42 + 3x3x3x3 = 123

Kool!


One of the Rap twins wrote:
if F(0)=2 then
F(n)=F(n-1)+3^(n-1)

the sequence becomes
n f(n)
0 2
1 3
2 6
3 15
4 42
5 123
6 366
7 1095
8 3282
9 9843
10 29526
etal.


Very Kool!



Jon's total charges at a local restaurant came to $386 last month. If he receives $5 off for each $25 that he spends, how much money did he have to pay?

Mark:
JON
$311

Before you ask, I am still struggling with the Whim problem. I have tried just about every permutation (except for the correct one). However, I am still convinced no other solution exists. Time will tell.
Thank you, stability returns. Or does it!

Rap:
Jon owes $386 and gets $5 credit for every $25. So the first reduction is
Int(386/25)=15 Remander of 11 so he pays $(15*20+11)=$311

So far we all agree. Then:

But under the rules this is greater than $25 and he gets a further reduction, and the second reduction is Int(311/25)=12 with a remainder of 11 so he pays $(12*20+11)=251

This is repeated until he finally owes less than $25. This takes 15 reductions and by my spreadsheet it figgered as

red/ amt/ n(386/25)/ rem/ n*20+rem
1 386 15 11 311
2 311 12 11 251
3 251 10 1 201
4 201 8 1 161
5 161 6 11 131
6 131 5 6 106
7 106 4 6 86
8 86 3 11 71
9 71 2 21 61
10 61 2 11 51
11 51 2 1 41
12 41 1 16 36
13 36 1 11 31
14 31 1 6 26
15 26 1 1 21

Finally after the 15 reduction the amount owed is less than $25


Jon pays $21

Well, that puts a spanner in the works. I think I will have to eat at this place. Great value and talking about value:


An oak rocking chair once owned by former President John F. Kennedy was sold in an auction for $442,500. This represents 8850% of its estimated value before the auction.

How many dollars was the estimated pre-auction value


What is the 2003rd positive odd number


The sum of three numbers is 98. The ratio of the first number to the second is 2:3, and the ratio of the second to the third is 5:8. What is the second number



A three-digit number is reversed, so that the units digit and the hundreds digit are interchanged, to form a larger number. The product of the two numbers is 65,125. What was the original number



From our European correspondent, see if this works better:

Serina is from Jamaica. The history student lives with her fiancée. The girl from the Philippines wants to be a nurse. Heidi studies economy. Annette lives with her father. The German girl lives alone. The Belgian girl studies Social Science. The engineer lives with her parents and a brother. Leena is not an engineer. The Phillipine doesn't live with any family. Leena is from Finland. Rina is from the Phillipines. The Belgian doesn't live in the dormitory.

Who lives in the dormitory


I know a word of letters three,
Add two and fewer there will be.

That word is


Give me food and I grow,
Give me drink and I die.

I am


Alive without breath,
As cold as death;
Never thirsty, ever drinking,
All in mail never clinking.

I am


Phew, if I have missed a response, tough luck I'm on holiday.

# BALLS
It is 7. The first six could have been split 2/2/2.

ROCKER
$5000

ODD NUMBER
4005

THREE NUMBERS
30

EXCHANGED DIGITS
125

WORD
few

FOOD/DRINK
fire?

Chair $5000 8850/100*$5000=$442,500 It musta been that Maloof chair

2003rd odd number is 4005=2(2003)-1

middle # is 30
x+y+z=98
x=2/3y y=5/8z so x=2/3*5/8z=10/24z
10/24z+5/8z+z=25/24z=98
so z=48 and y=5/8*48=30

125 or 521
(ABC)(CBA)=65125
AC*10000+B(A+C)*1000+(A^2+B^2+C^2)*100+B(A+C)*10+AC=65125
so AC=n*10+5 and AC+1=6 so A=1, C=5 & n=0
so B(A+C)=m*10+2 since A+C=6 B=2 and m=1
so ABC=125 and CBA=521
& (125)(521)=65125

Rina lives in the dorm (this was rushed)

That word---Fewer (this was telegraphed)

Rap

actually, i might be up to 3000 by now, if i hadn't wasted time on riddles.

Yitwail wrote, "actually, i might be up to 3000 by now, if i hadn't wasted time on riddles."

Sincere apologies, but the Doc said it was the only way to slow you down, and let me catch up


You guy's look far too good. Let us kick it up a notch.


A fire fighter is standing on the middle rung of a ladder. He moved up 9 rungs. The smoke got worse, so he moved back down 13 rungs. When the smoke cleared, he went up 19 rungs to the top. How many rungs does the Ladder have



A gardener has 36 poinsettia plants to ship to local florists. He ships them in boxes of 4 plants, or boxes of 3 plants. How might he ship all 36 plants if all boxes shipped must be full? How many solutions are possible



A multiple-choice test contains 40 items. A correct response earns 5 points, but 2 points are deducted for every incorrect response. Nothing is given nor deducted if the question is unanswered. Michelle scored 96. How might she have gotten this score
Find as many solutions as you can.

Firefighter
Ladder has odd number of rungs
so ladder has 2n+1 rungs Firefighter stands on the (n+1)th rung
so
2n+1=n+1+9-13+19
2n+1=n+16
n=15
so ladder has 31 rungs (2*15+1)

Poinsettia
4 possibilities
if x is # of 4 pot boxes
& y is # of 3 pot boxes
then 4x+3y=36
and x & y are positive integers
x+y=# of boxes
min # of boxes is 9
max # of boxes is 12
9 boxes---9, 4 pot boxes-- 0, 3 pot boxes
10 boxes--6, 4 pot boxes--4, 3 pot boxes
11 boxes--3, 4 pot boxes--8, 3 pot boxes
12 boxes--0, 4 pot boxes--12, 3 pot boxes

Michelle's test
R is # of right answers
W is # of wrong answers
N is # of no answer
R+W+N=40
5R-2W=96
R=(176-2N)/7=176/7-2N/7
176mod7=1
Rmod7=0
what (2N)mod7=1?
N=4,11,18,25
then
R=24,22,20,18
and
W=12,7,2,-3
but all answers (& no answers) have to be positive integers
so there are 3 possibilities
these are
R=24,22,20
W=12,7,2
N=4,11,18
for an score of 96.

Rap

LADDER
31

PLANTS
12*3, 0*4
8*3, 3*4
4*3, 6*4
0*3, 9*4
total number of solutions = 4

TEST
20 correct, 2 incorrect
22 correct, 7 incorrect
24 correct, 12 incorrect
total number of solutions = 3

Mark:

ROCKER
$5000

ODD NUMBER
4005

THREE NUMBERS
30

EXCHANGED DIGITS
125

WORD
few

FOOD/DRINK
fire

Clean sweep


Rap:
"It musta been that Maloof chair"

If you have a set, you are on to a sure thing.

2003rd odd number is 4005=2(2003)-1

middle # is 30

125 or 521

"Rina lives in the dorm (this was rushed)"

No excuses accepted, you are still right.


"That word---Fewer (this was telegraphed)"

We are here to help.



Li'l Turtle has $15.25 worth of nickels and dimes in her piggy bank. If she has an odd number of dimes and if she has more dimes than nickels, what is the largest number of nickels that she can have


I'm thinking of two secret numbers A and B.
A + B = -7
A - B = -17
What is the product of A and B


Rap got a fancy new digital watch for Christmas but he couldn't figure out how to set it. He figured out that his new watch was 5 hours and 38 minutes slow. If the correct time is 2:16 what time does his watch say


The perimeter of a square is 60% of the perimeter of a triangle whose sides measure 43, 47, and 50. What is the number of square units in the area of the square


The more you take, the more you leave behind.

I am


My first is a number, my second another,
And each, I assure you, will rhyme with the other.
My first you will find is one-fifth of my second,
And truly my whole a long period reckoned.
Yet my first and my second (nay, think not I cozen),
When added together will make but two dozen.

How many am I


What do you fill with empty hands


I will get to part II later. Off to Stonehenge now.

Li'l Turtle has 103 dimes and 99 nickles

The product of the two numbers is -60

Rap's watch says 8:38

The area of the square is 441

Time

The first is 4, the second 20 (but they don't Rhyme)

Applause

Rap

Challenge: choose 3 numbers and use only (-, /, *, +) and brackets if needed.

Rules:
You do not need to use all three numbers. Form expressions for the successive numbers from one up, until you can't go further. I did write numbers, and not digits.

What is the highest you can get?


For instance the numbers 1 2 3, have a break point 9.

1 = 1
2 = 2
3 = 3
4 = 1 + 3
5 = 2 + 3
6 = 1 + 2 +3
7 = 3 * 2 + 1
8 = 2 * ( 3 + 1)
9 = 3 * ( 2 + 1 )
10 not possible

Higest break point so far 17.

FIRST/SECOND
four and a score

??
10=3*3+1
11=3*3+2
12=(3+1)*3
13=(3+1)*3+1
14=(3*2+1)*2
15=(3+2)*3
16=(3+2)*3+1
17=(3+2)*3+2
18=3*3*2
19=3*3*2+1
20=(3+2)(3+1)

Rap

Of Course! No wonder my forehead is sloped.

Rap

Five day ago this problem was set by a cunning math wizard:





Whim had no problem with it. I however, have thought thro every available combination and failed miserably……

Until now, Eureka!



I weep no more.



Rap:

Li'l Turtle has 103 dimes and 99 nickles

The product of the two numbers is -60

Rap's watch says 8:38

The area of the square is 441



Mark:

FIRST/SECOND
four and a score


The riddles remain ?'sans' correct answers, although I did like ?'Applause'


Both Mark and Rap gave excellent answers to the Ladder/Flowers/Test.



Wanna bet?

Consider the toss of two coins and determine the following:

(a) What is the probability of at least one tail


(b) What is the probability of exactly two heads


(c) What is the probability of getting a head and a tail



Suppose that you know that your new neighbors have three children but you don't know the gender of these children. (Assume that the probability of a couple having a boy is equal to that of having a girl and there are no twins, triplets, etc.).

(a) What is the probability that there are two girls and a boy


(b) What is the probability that there are is at least one boy


(c) What is the probability that there are two boys and one girl given that you know that the first-born of the children is a girl


(d) What is the probability that there are exactly two boys given that you know that the first born is a boy