The worlds first riddle!

BUSES

?'Tricky'

"How many 1 foot by 1 foot bricks would it take to (complete)" = 1 the last one. :wink:

"How many times can you subtract the number 5 from 25"= Once, after that it is from 20,15 etc. :wink:

At last:
Inverter
Can a digital logic circuit with two inverters invert N independent inputs?
The circuit may contain any number of AND or OR gates.


Solution:
It can be shown that N inverters can invert 2^N-1 independent inputs,
given an unlimited supply of AND and OR gates. The classic version of
this puzzle is to invert 3 independent inputs using AND gates, OR
gates, and only 2 inverters.

This is solved by:
n1 = not(i1 and i2 or i1 and i3 or i2 and i3);
n2 = not((i1 or i2 or i3) and n1 or i1 and i2 and i3);
o1 = (i2 or i3 or n2) and n1 or i2 and i3 and n2;
o2 = (i1 or i3 or n2) and n1 or i1 and i3 and n2;
o3 = (i1 or i2 or n2) and n1 or i1 and i2 and n2;

i1, i2, and i3 are the inputs, n1 and n2 are the inverted signals, and
o1, o2, and o3 are the outputs. "and" has higher precedence than "or".

So, start with N inverters. Replace 3 of them with 2.
Keep doing that until you're down to 2 inverters.



A man is walking home with his dog at a steady 4mph. With 6 miles to go the dog is let off the leash and runs all the way home at 6 mph. The dog immediately turns and runs back to the man at the same speed, and upon meeting him it turns and runs home again. It continues to run back and forth at the same speed until the man reaches home.

What distance has the dog run since being let off the leash



Can you be mathematically certain that at least 100 people in the UK with a full head of hair have exactly the same number of hairs on their head and why

The dog will have run 6 mph * 1.5 hours = 9 miles.

Merlin, "1.5 hours = 9 miles."


A part of a wheel is a SPOKE, another word for people is FOLK, so how do you spell the word for the white of an egg

The desks of a classroom are arranged in rows. Each row has the same number of desks. Tom sits in the second row from the front, which is the fourth row from the back. His seat is the third from the left side and the fifth from the right side.

How many desks are in the room

HAIR
If the population of the UK is at least one more than 99 times the greatest number of hairs a person can have, then the pigeonhole principle tells us that there is some number of hairs that at least 100 people have.

EGG
w-h-i-t-e

DESKS
(2+4-1)*(3+5-1)=35

Mark wrote

HAIR
DESKS
EGG. Well, two out of three is not bad.

What is the ?'white' of an egg called? Not ?'white' surely.


My friends Grandma loved to make dumplings for her Grandchildren for Friday night dinner. She made enough for the children to get three(3) each. But this past Friday night, when she looked in the soup, she realized she had two (2) extra dumplings then she needed.

My friends father was very happy. Now he and his wife could have dumplings also, for a change, and if grandma was going to have some too, then there'd be enough for everybody to have two (2) each.

How many dumplings were there in total and how many children are in the family

DUMPLINGS

3C+2=2(C+3) ==> C=4
4 Children, 14 Dumplings

Mark sure knows his dumplings.

3C+2=2(C+3) ==> C=4
4 Children, 14 Dumplings


Answer: We know that everybody ate two dumplings. That makes six dumplings for the parents and the grandmother. Two of these six came from the two dumplings that were originally considered "extras." When we reduce the number of dumplings for each child from 3 to 2, we find there must be four children in the family. Total number of dumplings 14 = (4 x 3 + 2)


A woman got a job at a starting salary of $35,000 a year. If she received, an 8 percent raise each year. How much would her salary be at the beginning of the tenth year (to the nearest dollar.)


A five-digit number has the following characteristics:

no two digits are the same.
no occurs in the number.
the third digit is less than the second digit.
the second digit is twice the first digit.
the sum of the first four digits is divisible by 9.
the fourth digit is the square of the fifth digit.

What number am I


A man lived alone in a house for two months. Nobody came to visit him and he never went out. At the end of that time, he became deranged.

One night he put out the fire, turned off the lights, and walked out of the house. He was never seen or heard of again. His action in leaving that house resulted in the deaths of 90people.

Why was that

RAISE
There would have been 9 raises, so her salary would be $35,000*1.08^9 = $69,965.

5-DIGIT NUMBER
Ignoring the second clue, I reduced it to two possibilities:
36542
48693
I'll go with the latter assuming that 9 is meant to be the German for "no."

$69965/year

no occurs in the number?

Hew was a lighthouse operator.

Both Mark and Merlin arrived at the same correct amount.' $69,965.'

Mark was correct with his first calculation.
Answer: 36,542. The last clue gives possibilities for the fourth and fifth digits: 9 and 3 or 4 and 2. The third and fourth clues lead to the possibilities of 48,793 and 36,542, but the sum of the first four digits in 48,793 is not divisible by 9.

Merlin came up with ?'Lighthouse' don't ask me how, but he was correct.

He also asks, "no occurs in the number?"

The same number does not occur more than once in the answer.


A terrible crime has been committed and the police round up the usual suspects. During the interrogation of the four men the following accusations and statements are made:
Anderson said "Brimmers did it."

Brimmers said "Dodge did it."

Carter said "I didn't do it."

Dodge said "Brimmers lied when he said I did it."

If only one of the four men was untruthful, which man committed the crime

OT: Hi Mark, Bummer we can't pm anymore. I'll try it like this.

I was wondering if you had made any progress, with the programming project we talked about. If you still have my email address, you can contact me via that.

Btw, did you enter some of the contests at www.hadtoplayon.com?

Try: What's wrong with 48,693?

CRIME
Brimmers committed the crime and lied.

Deleted

Whim wrote, "I'll try it like this. Bummer" :wink:

Sorry Whim, it was Bimmers. As Mark wrote,

CRIME
Brimmers committed the crime and lied.

"What's wrong with 48,693?"

Upon re-reading the wording of the original question, I would say. ?'Nothing'.


There is a row a soldiers that is 1km in length. and they walk with a constant speed in a straight line, in 1 direction.

all the way at the end walks a messenger. he has to bring a message to the captain walking all the way at the beginning of the row

the messenger starts walking past the soldiers and immediately turns around when arriving at the captain and walks back to the end of the row. when the messenger is back at end. the hole group of soldiers traveled a distance of 1000 meters.

the soldiers and captain are walking at the same constant speed. and the messenger (walking faster then the soldiers) is also walking a a constant speed.

you don't know anything about time or speed.

question. how many meters did the messenger travel. from the end of the row to the beginning and back.


Ray's math teacher asked him to multiply three and four three times.
What is the correct answer

There is a new house. Everything in it is purple. The floors are purple, the walls are purple, the furniture is purple, the dog is purple and everything else.

What colour are the stairs

MARCH
2.4142 km

RAY
12 (each time)

PURPLE
purple

Mark wrote,

MARCH
2.4142 km

RAY
12 (each time)

PURPLE
purple


At last the remaining answers you seek.
After 120 seconds, will the lamp (the "infinity machine") be on or off
>>> Indeterminant - This procedure never makes it to 120 seconds.

IQ solution to: The infinity machine - a Gedanken experiment
It is obvious that the addition of 60 + 30 + 15 + 7.5 + ... converges to the value of 120. The addition of all elements up to infinity in fact leads to 120. But if you did an infinite number of switches, every time the lamp is on, it has to be switched off immediately. On the other hand, every time the lamp is off, it has to be switched on immediately!

Therefore, at 120 seconds the lamp is either on and off, or neither on or off?!

If "0" means the lamp is off and "1" the lamp is on, we can calculate the sum of the switching operations:
(+1 for switch on, -1 for switch off)
+ 1 - 1 + 1 - 1 + 1 - 1 ....

After 120 seconds, there is no result; instead this infinite sequence oscillates between two values (0 and 1). That means were are able to determine the status of the lamp for every time point before 120 seconds, but not for 120 seconds (or later). This is simply because an infinite sequence does not have a last term.

In other words: It is true that the lamp has to be on or off after 120 seconds, but we are not able to find out which is the case!



A casino in Las Vegas: You want to join a game with three cards. One is white on both sides, one is red on both sides, and the third is white on one and red on the other side. Every card is in a black case. You have to chose one of these cases and pull out the card so you can see one side of the card.

Let's say the visible side of the card is white. The banker offers you a bet of 50:50 that the back side is also white.

Would you play this game?
>>> No - the probability of other side being white is 2/3

IQ solution to: Playing cards in Las Vegas
You may think as follow: "The back side has to be either red or white, that sounds fair, the probability is 50 %." But this is wrong.

As mentioned, we have three different cards. But the fact that one visible side is white does not mean that both possibilities do have the same probability. There are overall three white card sides: one has a red back side, and both others are the front and the back of the same card; i.e. white-red, white1-white2, and white2-white1. The conclusion is that the probability for a white back side is 2:3 or 66,67 %, and not 50:50. If you play enough games against the banker, he will bleed you dry for sure.


Two flies are sitting on a column, one at the bottom (x) and the other at the top (y). The distance between them is 126 cm. The column is decorated with a stripe which is winded 3.5 times around the column. The stripe has a bottom silver border and a top golden border. The column's circumference is 48 cm.

Suddenly, the bottom fly starts crawling from point x (the lowermost end of the golden border) along the golden border. At the same time, the other fly at y (the uppermost end of the silver border) crawls downwards along the silver border.

What distance have the flies covered when they are at the same height?
>>> 105 cm each


Each fly has crawled 105 cm.
This can be seen when the column surface is uncoiled. The short site is the circumference (48 cm), the long site is equivalent to the height (126 cm). The height gives place to 3.5 windings of the stripe, or 126 : 3.5 = 36 cm per winding.

The golden border is the hypotenuse of a right-angled triangle with the legs of 36 cm and 48 cm, respectively. Using Pythagoras' theorem, the length of the hypotenuse is 60 cm. Hence, the length of the golden (and also the silver) border is 60 cm × 3.5 = 210 cm. Half of this length is the distance that each fly has crawled, which then have the same distance from the ground (they arrive at the points x1 and y1).




Can you arrange the odd digits 1, 3, 5, 7, and 9, and the even digits, 2, 4, 6, and 8, in such a way that the odd ones add up to the same as the even ones

You can use arithmetical signs and decimals, but the idea is to try and arrive at the simplest possible solution. There are, of course, many possible answers.

What is the four-digit number (no zeros) in which the third digit is the number of "winds," the first digit is one-half of the third, the second digit is double the third and the last digit is one-half the sum of the first three

I am on three legs when I rest and one when I work.
What am I

WINDS
2847

DIGITS
13+5-7+9 = 2+4+6+8

Thanks for the old ones.

Mark, no problemo. However this is the last file, then it is back to the drawing board. Or, should that be ironing board?.

WINDS
2847 How did he do that?

DIGITS
13+5-7+9 = 2+4+6+8

1 + 3 + 7 + 9/5 = 12.8 and 2 + 4 + 6 + .8 = 12.8

What would be the next number in the following sequence
11 1,331 161,051 19,487,171 ?

The square of 13 is 169. Take the last digit of the square, 9, and place it in the middle, making 196. This is the square of 14, the next number above 13.

What are the next numbers, which also have this property

Here on Earth it's almost always true, that tomorrow will follow today.
Yet there is a place where yesterday always follows today.

Where is this place

SEQUENCE
2,357,947,691

SQUARES
157^2=24649, 158^2=24964

YESTERDAY
The dictionary

Mark wrote,
"SEQUENCE
2,357,947,691

SQUARES
157^2=24649, 158^2=24964

YESTERDAY
The dictionary "

Words fail me. If it was not for the fact that I get up early you would have the answers and I would have to work out the questions. The last person who was as consistent was the great Iacomus.

2,357,947,691. The numbers are 11 to the first power, 11 to the third power, 11 to the fifth power, 11 to the seventh power; so the missing number is 11 to the ninth power.

157 squared is 24649, and 158 squared is 24964.


There are several ways to come up with 100 by using the digits 0 through 9. One way is: 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + (8 x 9) = 100. Another way is 78 3/6 + 21 45/90.

Can you come up with 2 more ways

If 1/2 of 16 were 13, what would 1/3 of 32 be

Eilah is now two-thirds of Sally's age. In six years, Eilah will be four-fifths of Sally's age. In 15 years, Eilah will be seven-eighths as old as sister Sally.

If they are both under the age of ten, how old are they now