The worlds first riddle!

3x3x3 cube:

I get 90.

Centers are always one, edges will show a one and a two, corners will show a one, two, and three.

Six centers = 6
12 edges = 12*3 = 36
eight corners = 8*6 = 48

6+36+48=90

3 dice:

1/2. A simple way to visualize: It doesn't matter what the sum of the first two dice is. The third die will always determine if the sum is odd or even, and you have a 50/50 chance of getting an odd or even number.

EIGHT
14 (6,6,6,8,8,8,8,14)

Mark
ANTIFREEZE
11:7

DISCOUNT CARD
15% ($100 purchase)

EIGHT
14 (6,6,6,8,8,8,8,14)



Merlin
3x3x3 cube:

I get 90.

3 dice:

1/2.




Two twelve-hour clocks were both wound up and started at 12:00 noon.
One clock loses 10 minutes every hour, and the other gains 10 minutes
every hour. Both clocks now show the same time.

What is the correct time


Mary's age is twice Fred's age and one-third of Sally's age. If the sum of their ages is 99, how old are the three friends


At what speed, in miles per hour, does a point at the earth's equator spin around the earth's axis


A fair die is tossed four times. What is the probability that it lands with either 5 or 6 on top at least once



I am carrying out some research into the distance of: 316 feet or 96.3168 meters.

For example, the following all measure that distance:

Crop circles
July 20 (?) - College Ward,(50 miles north of Logan) Utah. "Circles,
rings and pathways". 316 feet diameter.

Big Ben. London England.
The tower is 316 feet high.

June 1st 1900, Victoria Pier officially opens. 316 feet in length,

Wind Turbines. Scotland.
16 wind turbines are proposed, with a capacity of up to 1.75 megawatts and an overall height to blade tip of up to 316 feet.

Building, Washington, D.C.'s Old Pension Building.
The Great Hall is 316 feet.

Paris. France:
Europe's first skyscraper, its clock tower reaching a height of 95 metres (316 feet).

Michelangelo's Palazzo Farnese in Rome, complete with huge, Corinthian
columns and an enormous, central hall 316 feet long,


Sikh Temple
One facade is 316 feet long.

BFI applied for a permit from the Texas Commission on Environmental Quality in April to expand vertically to 316 feet.

Budapest:
... With a dome standing at 316 feet.

Russia:
The Pecherskaya Lavra (The Monastery of the Caves) Bell Tower built between 1731 and 1745 is the tallest bell tower in Russia standing 316 feet.

There are hundreds of other examples.


Any (sensible) suggestions as to why this particular number has worldwide properties?

A) For the same reason someone holds up a "John 3:16" sign at every sporting event.

For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.

B) Coincidence

C) ?

TIME
12:00 midnight

AGES
Fred is 11, Mary is 22, Sally is 66

SPEED
Roughly 1000 mph

DIE
65/81

Tiger, thank you. I think you have cracked it. A cheque is in the post. :wink:

Mark, who needs to be checked wrote:

TIME
12:00 midnight

AGES
Fred is 11, Mary is 22, Sally is 66

SPEED
Roughly 1000 mph

DIE
65/81


Now check these out.

On a recent front page of the Philadelphia Inquirer there was a story about a new dollar coin and the promotion it is going to get.

"The coin will first become available inside boxes of Cheerios. In that promotion 10 million boxes of Cheerios will be packaged with a new dollar coin in every 2000th box, and a certificate for 100 coins in every 4400th box."

How many coins will the government give away in this promotion

This problem was suggested by Stephen Maurer, a math professor at Swarthmore College.


876+429 = 1305 is one way to write a sum which uses all digits (0-9) only once. How many different ways are there to do this


When an ice cube melts in a glass of water, does the level of the water fall or rise

Dollar promotion:

Assuming that all certificates are claimed: 232,200.

Ice Melt:
The water level stays the same.

"876+429 = 1305 is one way to write a sum which uses all digits (0-9) only once. How many different ways are there to do this?"

That sounds like the kind of question Whim asks.

How about figuring out how many equations you would have to check if you were to try all possible combinations? To make it easier, allow a leading zero and count rearrangements as different.

I get
10! * [SUM for N=1 to 8 of (2^N) - 1]
= 10! * [(2^9) - 10]
= 10! * 502
= 1,821,657,600
The font size is four in case you don't want to see it before you solve it.

a quarter and 5 cents (whatever Americans call that coin)

Water level:

Water is at its most dense at 3.97°C. The water level would drop almost infinitesimally, and then rise again.

A nickle.

Try:
Just to be clear, my 10 widget number doesn't answer the question you posed. It should answer the question I posed.

DATES
The folks born in 1980 will make the boast in 2025.

PAINT

Try said: "876+429 = 1305 is one way to write a sum which uses all digits (0-9) only once. How many different ways are there to do this?"

Progress report: There are 94 different numbers that can appear on the right side of the equation. They range from 36 to 6021. If rearrangements of terms on the left side count as different solutions, there are 398,472 solutions. I'm still working on the number of solutions without rearrangements. It will be considerably smaller.

My dear MyO, How is the weather over in old Europe?
Q. " Two US coins are worth 30 cents and one is not a quarter."

A. " a quarter and 5 cents"

Do you want to stick with that answer, or twist?


Merlin:
Water level:

"Water is at its most dense at 3.97°C. The water level would drop almost infinitesimally, and then rise again."

He is good, very good!

Actually, it will then fall for two reasons:

• Water actually contracts when its temperature rises from 0°C to approximately 3.98°C. (Beyond that point, water expands when temperature rises, just like most substances do.)

• The cross-section of the container increases with temperature, so that a volume of water which decreases or remains constant will have less height. This argument shows that the water level will continue to decrease (at least initially) at the 3.98°C point.

Of course, we assume that the level is measured from the bottom of the container with instruments not sensitive to temperature (beware of rulers). The contraction is minute and will not be observed in the kitchen, but this would be readily measured in the lab with precise enough instruments... When the cube was not yet fully melted, the temperature remained constant (0°C) and even a temperature-sensitive ruler would have "shown" the level to remain constant.


Mark:
"Just to be clear, my 10 widget number doesn't answer the question you posed. It should answer the question I posed."

In a heroic effort to rise the standard, Mark has taken to answering his own questions. Which is just as well, I doubt anyone else could. :wink: My mistake, I only caught the last line. Your proof is impeccable as always.

Paint:
11 17 13 19 15
6 2 8 4 10
16 12 18 14 20
1 7 3 9 5


My answer:

13 9 19 7 11
5 1 14 3 17
16 10 20 8 12
6 2 15 4 18


I wonder how many solutions there are.


Mark continues (in code):
DATES
"The folks born in 1980 will make the boast in 2025."

Needless to say, he is right.



What is the logic in this sequence of numbers below

8 5 4 9 1 7 6 10 3 2 0



Does this (number) mean anything:

"Now, I know a magic utterance to assist maths"



This sentense contains two mistakes. What are the mistakes



Take the wives of Henry VIII of England, multiply that number by the number of dwarfs that befriended Snow White, divide by the number of seas, and multiply by the number that represents "love" in tennis.

What is your answer



If 6 is 5, and 7 is 8, and 10 is 5 too, what is 9

SEQUENCE
The numbers are in alphabetical order.

UTTERANCE
The lengths of the words represents the digits of pi in order.

WIVES
0

MISTAKES
One spelling and error and one numerical error (or is it an error?).

Mark in fine form (and before 9am).

SEQUENCE
The numbers are in alphabetical order.

UTTERANCE
The lengths of the words represents the digits of pi in order.

WIVES
0

MISTAKES
One spelling and error and one numerical error (or is it an error?).

Yes, as there is only the spelling error, to say there are two errors, is the second error. :wink:


Numbers:
The answer, I thought, is 48. Listed below are the basic 6 pairs of solutions. Each of these represents 4 distinct solutions obtained by switching digits between the two summands. (We count as distinct only different pairs of summands, not the same pair in a different order.)


879+426=1305 & 879+624=1503
859+347=1206 & 859+743=1602
789+264=1053 & 789+246=1035
756+342=1098 & 765+324=1089
657+432=1089 & 675+423=1098
589+473=1062 & 589+437=1026




I recently met six men and they each had six baskets. Each basket has six cats inside and each cat had six kittens. Assuming all are whole and healthy, how many legs are there in this unusual group


If you're geographical position was 0° latitude, 0° longitude, where in the world would you be

(A) At the Greenwich Observatory in England
(B) In the Atlantic Ocean
(C) In the West African country of Ghana
(D) At the center of the Earth
(E) Somewhere else


What number when spelled out has each of the vowels (not including Y) and no repeated letters

Legs:
6060

Geographical Position:
I would venture c) but I'll have to check.

Edit: Nope. It's below Africa's western lobe.

NUMBERS
I thought the problem was to find all solutions, not just those of the form ###+###=####. That simplifies matters greatly. Are you sure the mathematician didn't intend for all solutions to be counted? It hardly seems worth posing in the limited case.

VOWELS
Five Thousand