The worlds first riddle!

Re the pigeons I'm thinking the downward air pressure from the pigeons wings in flight may maintain the same weight ie weight of each individual pigeon is lifted by pushing air down. the increased air pressure is similar to pointing a compressor nozzle at a scale. However it may depend on how airtight the van is.

I'm probably showing my ignorance here but willing to learn something besides how to crack a tinny.

Possibly your shout TA?

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Does the total weight of the van and pigeons change ?

Whilst I am no physics professor, I have to agree with DP when he said, "I'm thinking the downward air pressure from the pigeons wings in flight may maintain the same weight ie weight of each individual pigeon is lifted by pushing air down." Cool

I think you are right, the weight doesn't change because the birds were being supported by the van before and by the air within it after, so it both cases the weight is equal to the sum of that of the van plus the pigeons. However, I have been wrong in the past, or so I?'ve been told.

DP, "I'm probably showing my ignorance here but willing to learn something" Shocked

I thought you were gonna be lernin us! After all, are you not the land of; Rolf Harris, Crocodile Dundee and Ned Kelly?

"Possibly your shout TA?"
What shores?

Well thank you for askin, make mine a Red Lion. Laughing

Let's try:

You are in a stopped car with a helium balloon floating in the passenger compartment. All the windows are closed. The car accelerates forward. With respect to the passenger compartment, does the balloon move:

Forward Question

Backward

Or stay stationary Question

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Quote:

yes.. Down
Does anyone agree with this answer?

Well, there were only two options; up or down. The weight can never get up, so it must be down. Smile

Perhaps it a play with words, and are the birds loosing so many feathers, the weight is the weight of the feathers (down).

The real answer will probably say: the weight stays the same.

Whim

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[size=7]BALLOON
forward

BIRDS
same[/size]

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[size=7]8X8 GRID
1 2 3 4 * 6 7 8
2 3 * 5 * 7 8 9
3 4 5 6 7 8 * 0
* * 6 7 * 9 0 1
5 6 7 * 9 0 * *
6 * 8 9 0 1 2 3
7 8 9 * 1 * 3 4
8 9 0 * 2 3 4 5[/size]

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markr wrote:

8X8 GRID
1 2 3 4 * 6 7 8
2 3 * 5 * 7 8 9
3 4 5 6 7 8 * 0
* * 6 7 * 9 0 1
5 6 7 * 9 0 * *
6 * 8 9 0 1 2 3
7 8 9 * 1 * 3 4
8 9 0 * 2 3 4 5

Is it a unique solution, Mark?

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Mark:

BALLOON
Forward Cool

Desired Response: The balloon will move forward in the passenger compartment because inertia forces the air molecules back, creating low pressure up front into which the balloon moves. Try it. Laughing

BIRDS
Same Cool

Whim:The real answer will probably say: the weight stays the same. Cool

Mark:

8X8 GRID Cool

1 2 3 4 * 6 7 8
2 3 * 5 * 7 8 9
3 4 5 6 7 8 * 0
* * 6 7 * 9 0 1
5 6 7 * 9 0 * *
6 * 8 9 0 1 2 3
7 8 9 * 1 * 3 4
8 9 0 * 2 3 4 5

I don't freekin believe it! I have already prepared a set of hints, as I mistakenly thought an early reply was not to be anticipated. Congrats Mark. BTW The answer is unique.

There's a fishbowl with 200 fish and 99 percent are guppies. How many guppies do you need to remove to get to the point where 98 percent of the remaining fish are guppies Question

True or False?
The product of any two 4 digit numbers is an 8 digit number Question

A stick is marked with a red marker into 7 equal parts (6 red marks), and by a blue marker into 17 equal parts (16 blue marks). It is then cut into 24 equal pieces.

Is it possible that each piece has exactly one colored mark on it Question

(Please note: This problem is hard, if you are on medication - DO NOT ATTEMPT)

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guppies= remove 100 guppies

Product of two 4 digit number = no 1000*1000=1,000,000 7 digits

coloured marks= The bride says nope. Used a stick that was 2856 cm long. Cost me a packet for the paint and near took her hand off with the circular saw. She gave up after that.

For sale 1/2 tonne fire wood Smile

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G'Day DP, I see you decided to let your sheila give circular saw a burl. Seems like she made a bit of a blue, I don't want to knock, but has she a kangaroo loose in the top paddock?, No worry, she'll be right. I hope you came out ok, why not chuck a sickie and give yourself a bit if time to hit the turps. Laughing

Sorry about the lumber, I am in a smoke free zone. Rolling Eyes

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The grid was quite easy. Any digit in any location determines the whole grid; so there are only ten arrangements to consider.

[size=7]STICK
A variant of this is the current problem at another site I frequent. The numbers there are 13, 17, 30.

Each piece (except the two end pieces) will have exactly one color on it. I wrote a program that demonstrated this to be true when the largest number ranges from 5 to 1000 and the smaller numbers are relatively prime and sum to the largest number. I don't know the proof (I'm hoping you'll supply one), but I'd bet it's true for all numbers greater than 1000.[/size]

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Tryagain wrote:

I have to admit I am going round in circles. I thought it was 10 decibels=1 bel.

The 100=1. half of 10 is 1. (=) v (is) sure is a puzzler. Therefore, I say the answer is. ?'L'

A van containing pigeons on perches is being weighed on a scale. Something scares the pigeons and they all begin flying around inside the van.

Does the total weight of the van and pigeons change
If so;

Up
Down

(=) v (is) was a red herring. I'll give a hint: think bases and modulo.

As for the pigeons, the weight will go down - Earth's gravitational field decreases with height. Shifting the center of mass upwards will decrease the weight ever so slightly Very Happy

Ignoring that and assuming the van is a closed system, the weight will stay the same, but I'm not sure we can say the same about the scale reading. Which way it would go initially, I can't say.

Tryagain wrote:

A new 8 x 8 puzzle.

RULES:

Use 0-9

Each number MUST have its digits in consecutive INCREASING order, both across and down. With 0 being allowed to follow 9.

EG. 901, 890123, etc. Of course, a number may NOT begin with a 0.

A digit may be used only ONCE each line.

The _ represents a space for a digit.

The * represents a block. (Just like a crossword)

_ _ _ _ * _ _ _
_ _ * _ * _ _ _
_ _ _ _ _ _ * _
* * _ _ * _ _ _
_ _ _ *_ _ * *
_ * _ _ _ _ _ _
_ _ _ * _ * _ _
_ _ _ * _ _ _ _

This one was driving me crazy because I thought the numbers before and after the * had to be consecutive (eg, 12*3...). I couldn't figure out how it wasn't impossible Shocked

I thank mark for putting me out of my misery.

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Dadpad:

guppies= remove 100 guppies Cool

Product of two 4 digit number = no 1000*1000=1,000,000 7 digits Cool

Well done mate, lucky guess. twice! Laughing

Mark:

STICK
A variant of this is the current problem at another site I frequent. The numbers there are 13, 17, 30.

There are other sites out there? Shocked

Each piece (except the two end pieces) will have exactly one color on it. I wrote a program that demonstrated this to be true when the largest number ranges from 5 to 1000 and the smaller numbers are relatively prime and sum to the largest number. I don't know the proof (I'm hoping you'll supply one), but I'd bet it's true for all numbers greater than 1000.

Sure, I will supply one. However, I will not be taking any bets.

We are marking with the points on the number line 1/7,2/7,3/7,4/7,5/7,6/7 and with blue 1/17,2/17,...,16/17. First check that we never mark the same point both red and blue: i/7 could not equal j/17, if i is less than 7 and j is less than 17. So we have made exactly marks in 22 different locations.

We are cutting at 1/24,2/24,3/24,...23/24. The first piece from 0 to 1/24 does not contain 1/7 or 1/17 so it has no marks, as does the last piece from 23/24 to 1. This leaves 22 pieces and 22 marks.

We show that no piece has two marks on it, so each piece must have exactly one mark.

Since each piece has length 1/24 which is less than 1/17 and less than 1/7, each piece could contain at most red mark and one blue. Could both be on a single piece? If so, call them i/7 and j/17, and they are adjacent marks. However the number (i+j)/24 is between these two fractions, so our stick was cut at this location and i/7 and j/17 are not on the same piece.

Exe ?'X':

"(=) v (is) was a red herring" Shocked

No way are ?'newbies' allowed to trick the inflicted. First public warning. :wink:

"I couldn't figure out how it wasn't impossible"

Think positive. Laughing

"I thank mark for putting me out of my misery"

That's easy for you to say, each correct answer compounds my misery. Twisted Evil

I.R.S. ability test.

Who has more money Question

Person A starts with $1000, the first year it increases by 8%, the next year by 10%, and the third year by 12%.

Person B has increases of 10%, then 12%, then 8%.

True or False Question

If an integer which ends in a 3 is divided by 17, the remainder is non-zero.

True or False Question

To multiply any number x by 99, all we do is attach 2 zeros at the end of the decimal expression for x, and then subtract x.

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Tryagain wrote:

Exe ?'X':

"(=) v (is) was a red herring"

No way are ?'newbies' allowed to trick the inflicted. First public warning. :wink:

I'm showwy Embarrassed

Tryagain wrote:

I.R.S. ability test.

Who has more money

Person A starts with $1000, the first year it increases by 8%, the next year by 10%, and the third year by 12%.

Person B has increases of 10%, then 12%, then 8%.

True or False If an integer which ends in a 3 is divided by 17, the remainder is non-zero.

True or False To multiply any number x by 99, all we do is attach 2 zeros at the end of the decimal expression for x, and then subtract x.

IRS: Depends on how much B starts with?

False: 9*17=153

False: 1.5 * 99 != 1.500 - 1.5

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X marks the spot:

"IRS: Depends on how much B starts with?"

Dagnabit! The same as ?'A' Embarrassed

I'm showwy 2.

"False:"

"False:"

Well, one outta two aint bad! Laughing

If you can answer this; I will run round Times Square nakid!

Answer each of the 8 questions with a letter from A to D.

The word "answer" in the test refers to YOUR answer, not some hypothetical "best" answer.

After choosing, the 8 answers score the test by comparing each question with your answers.

Score 1 point for each question answered correctly, 0 otherwise.
Keep re-taking the test, trying to get the highest possible score.

(Of course you must know what the highest possible score is in order to correctly score the last question!) Twisted Evil

(1) The next question with the same answer as this one is:
(A) 2 (B) 3 (C) 4 (D) 5

(2) The first question with answer C is:
(A) 1 (B) 2 (C) 3 (D) 4

(3) The last question with answer A is:
(A) 5 (B) 6 (C) 7 (D) 8

(4) The number of questions with answer D is:
(A) 1 (B) 2 (C) 3 (D) 4

(5) The answer occuring the most is: (if tied, first alphabetically)
(A) A (B) B (C) C (D) D

(6) The first question with the same answer as the question following it is:
(A) 2 (B) 3 (C) 4 (D) 5

(7) The answer occuring the least is: (if tied, last alphabetically)
(A) A (B) B (C) C (D) D

(8) The highest possible score on this test is:
(A) 5 (B) 7 (C) 6 (D) 8

Ha ha. Ha ha etc

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IRS
Multiplication is commutative; so they are the same.

MULTIPLICATION BY 99
If the problem were restated as:
"To multiply any number x by 99, all we do is move the decimal point of x two positions to the right, and then subtract x."
it would be true.

Thanks for the proof. It's rather simple.

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[size=7]8 QUESTIONS
Score = 7
Question#, Answer, Points
1. C 1
2. A 1
3. D 1
4. C 1
5. D 1
6. D 1
7. B 1
8. A 0[/size]

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Problem: If 100=1 and half of 10 is 1, what is half of 100 Question

Bearing in mind I flunked ?'Math for dummies', I propose this solution to the problem:

N
Sum[ x ] = N2/2+N/2
x=1

Mathematical Induction can be used in the following manner to prove this relation true.

Step 1: Show that the first case is true. So, set N equal to 1.

1

Sum[ x ] = 12/2+1/2
x=1
1 = 1/2+1/2
1 = 1 True!

Step 2: Show that the subsequent cases are true. So, set N to the value N+1.

N+1
Sum[ x ] = (N+1)2/2+(N+1)/2
x=1
N
Sum[ x ]+(N+1) = [(N2+2N+1)+(N+1)]/2
x=1

(N2/2+N/2)+(N+1) = (N2/2+3N/2+1)
(N2/2+3N/2+1) = (N2/2+3N/2+1)

Proof Complete Razz

Or is it?

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Tryagain wrote:

"False:"

"False:"

Well, one outta two aint bad!

Hmm..."If an integer which ends in a 3 is divided by 17, the remainder is non-zero" depends on which integer, maybe Idea

Tryagain wrote:

If you can answer this; I will run round Times Square nakid!

Answer each of the 8 questions with a letter from A to D.

The word "answer" in the test refers to YOUR answer, not some hypothetical "best" answer.

After choosing, the 8 answers score the test by comparing each question with your answers.

Score 1 point for each question answered correctly, 0 otherwise.
Keep re-taking the test, trying to get the highest possible score.

(Of course you must know what the highest possible score is in order to correctly score the last question!)

(1) The next question with the same answer as this one is:
(A) 2 (B) 3 (C) 4 (D) 5

(2) The first question with answer C is:
(A) 1 (B) 2 (C) 3 (D) 4

(3) The last question with answer A is:
(A) 5 (B) 6 (C) 7 (D) 8

(4) The number of questions with answer D is:
(A) 1 (B) 2 (C) 3 (D) 4

(5) The answer occuring the most is: (if tied, first alphabetically)
(A) A (B) B (C) C (D) D

(6) The first question with the same answer as the question following it is:
(A) 2 (B) 3 (C) 4 (D) 5

(7) The answer occuring the least is: (if tied, last alphabetically)
(A) A (B) B (C) C (D) D

(8) The highest possible score on this test is:
(A) 5 (B) 7 (C) 6 (D) 8

Ha ha. Ha ha etc

The highest possible score on the test is 7, but that can only be achieved by getting question (8) wrong Very Happy

The solution is unique: C-A-D-C-D-D-B-A

Tryagain wrote:

Problem: If 100=1 and half of 10 is 1, what is half of 100

Bearing in mind I flunked ?'Math for dummies', I propose this solution to the problem:

N
Sum[ x ] = N2/2+N/2
x=1

Mathematical Induction can be used in the following manner to prove this relation true.

Step 1: Show that the first case is true. So, set N equal to 1.

1

Sum[ x ] = 12/2+1/2
x=1
1 = 1/2+1/2
1 = 1 True!

Step 2: Show that the subsequent cases are true. So, set N to the value N+1.

N+1
Sum[ x ] = (N+1)2/2+(N+1)/2
x=1
N
Sum[ x ]+(N+1) = [(N2+2N+1)+(N+1)]/2
x=1

(N2/2+N/2)+(N+1) = (N2/2+3N/2+1)
(N2/2+3N/2+1) = (N2/2+3N/2+1)

Proof Complete Or is it?

I'm a little confused about your notation. What do you mean by N2?

Anywho, the answer I was looking for was...

10. It's all modulo 3 in binary. 100 is 4, which is congruent to 1 mod 3. Half of 10, or 2, is also 1. In the end, the answer isn't changed by the fact that it's mod 3.

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Boy, it sure was cold in Times Square this morning. Mr. Green

Mark:

8 QUESTIONS
Score = 7 Cool

Question#, Answer, Points
1. C 1 Cool

2. A 1

3. D 1

4. C 1

5. D 1

6. D 1

7. B 1

8. A 0

Logic Test --- Solution CADCDDBA

The unique highest possible score is 7, and it can only be obtained by answering the last question wrong! Three cheers for Mark. Razz

MULTIPLICATION BY 99
If the problem were restated as:

"To multiply any number x by 99, all we do is move the decimal point of x two positions to the right, and then subtract x."

"It would be true." Cool

True, very true.

"Thanks for the proof. It's rather simple."

When you know the answer, the question is always simple. Laughing

X:

"Hmm" :wink:

You are soooo polite. Mark has re-worded the question to match my answer.

"The highest possible score on the test is 7, but that can only be achieved by getting question (8) wrong The solution is unique: C-A-D-C-D-D-B-A"
Three further cheers for X.

I see you are a wizard in waiting. Razz

"10. It's all modulo 3 in binary. 100 is 4, which is congruent to 1 mod 3. Half of 10, or 2, is also 1. In the end, the answer isn't changed by the fact that it's mod 3." Cool

Fairynuff, you win. I would never have got to that answer. My only comfort is no one else did either. Laughing

Fairy Nuff asks:
What is the smallest number with every digit = 1 or 0 that is divisible by 225 Question

The numbers 1 up to and including 8 must be put in the circles of the depicted net. However, numbers in neighbouring circles must differ more than 1.

For example, circles connected to a circle with a 4 may not contain a 3 or a 5.

Can you meet the challenge Question

* 0 0 *
0 0 0 0
* 0 0 *

It's always 1 to 6,
it's always 15 to 20,
it's always 5,
but it's never 21,
unless it's flying.

What am I Question

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[size=7]CIRCLES
* 3 5 *
7 1 8 2
* 4 6 *[/size]

225
Smallest positive integer?

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The worlds first riddle!

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