The worlds first riddle!

[size=8]FACTORIAL
10

TREE/BUSH
If I understand the lines correctly:
.........1
......8...10
...6....7....5
3....4....9....2[/size]

Happy holidays, and thanks for the puzzles this past year!

Thank you Mark for your kind words, the pleasure has been mine. I think we will make it into the forth year.




Below there are sixteen numbers. Assuming that any three of the numbers may be drawn at random, what are the chances that three numbers will be drawn whose sum equals six


1 2 3 1
2 3 1 2
3 1 2 3
1 2 3 1





Divide 30 by 1/2 and add 10

What is the answer

[size=8]SIXTEEN NUMBERS
3: 1/28
4: 15/112
5: 27/112
6: 2/7
7: 11/56
8: 5/56
9: 1/56

Divide 30 by 1/2 and add 10
70[/size]

Mark:

SIXTEEN NUMBERS
3: 1/28
4: 15/112
5: 27/112
6: 2/7
7: 11/56
8: 5/56
9: 1/56


This was a bit tricky and I initially thought the answer was 1/16 or 6.2% but Mark is right, it is really 2/7 or 28.6%.

Either rolling '2 2 2' or some combination of '1 2 3' adds up to be 6. The chances of getting '2 2 2' are 5/16 (5 2s out of 16) times 4/15 (4 2s left out of 15) times 3/14 (3 2s left out of 14). This is 5/16 * 4/15 * 3/14 which equals 1/56.

The chances of getting some combination of '1 2 3' is equal to 6/16 (6 1s in the list) times 5/15 (5 2s out of 15 numbers left) times 5/14 (5 3s out of 14 numbers left) times the number of different combinations of '1 2 3' which is 6. This is 6/16 * 5/15 * 5/14 * 6 which equals 15/56.

1/56 + 15/56 = 16/56 or 2/7 or ~28.6%.



Divide 30 by 1/2 and add 10
70

Not a lot of people know that. Well they do now!



The A2K Christmas Riddle quiz-

You must determine the values of A, B, C, D, E, F, G, H, and I in the magic square (3x3). The magic sum is equal to Elvis' age when he died. (But he really lives)

The nine clues about Elvis' life should be all that you need to solve this magic square. However, it can be solved mathematically with just a little logic.

The sum of the three numbers in each row, column, and diagonal must all be the same.

In the clues below, the day refers to a number from 1 to 31 -- not the names of the days of the week.

Clues:
A. The number of weeks that Elvis' Blue Hawaii album stayed at #1 on the charts.
B. Elvis' height measured in feet.
C. The day in August 1977 on which Elvis died.
D. It was on this day in April of 1957 that Elvis moved in to Graceland.
E. The number of times that Elvis was nominated for a Grammy Award.
F. The number of Elvis' top 40 hits that hit #1 (he had 107 top 40 hits).
G. The day in May 1960 of Elvis' television special, "Welcome Home, Elvis."
H. Elvis' age when he moved into Graceland.
I. The day in January 1935 on which Elvis was born.




For those of you who are not of a musical persuasion:

Now, we have all heard about n items x3 weightings etc. So let's have something different:

There are 8 balls.

Seven balls are the same; the 8th is slightly heavier than the rest.
You also have a balance-scale (the one with a platform on either side) but it has no markings on it.

Using the scale only TWICE, locate the ball that is heavier


It can be done, I have done it already.

My brain hurts now.

[size=8]BALLS
3 vs 3
if equal, 1 vs 1 with the remaining 2 (done)

if not equal, 1 vs 1 with 2 from the heavier set of 3
if 1 vs 1 is equal, the third is heavier, otherwise the heavy one is heavier (done)[/size]

Magic sum, and age of Elvis when he died: 42

A. The number of weeks that Elvis' Blue Hawaii album stayed at #1 on the charts. (20)
B. Elvis' height measured in feet. (6)
C. The day in August 1977 on which Elvis died. (16)
D. It was on this day in April of 1957 that Elvis moved in to Graceland. (10)
E. The number of times that Elvis was nominated for a Grammy Award. (14)
F. The number of Elvis' top 40 hits that hit #1 (he had 107 top 40 hits). (18)
G. The day in May 1960 of Elvis' television special, "Welcome Home, Elvis." (12)
H. Elvis' age when he moved into Graceland. (22)
I. The day in January 1935 on which Elvis was born. (8)

Howdy Lordy, it's not everyday we receive a visit from royalty. If it's the sauna you seek, try second on the left at the end of the corridor, you will find Gus in there with one of the Chicks from Trivia and a large rodent.


BTW your Spanish, she is very good! However, your selection! Mamma Mia!!! :wink:

Mark:

BALLS
3 vs 3
If equal, 1 vs 1 with the remaining 2 (done)

If not equal, 1 vs 1 with 2 from the heavier set of 3
If 1 vs 1 is equal, the third is heavier, otherwise the heavy one is heavier (done)

Well, I thought it was difficult.


Stormy:

Magic sum, and age of Elvis when he died: 42

A. The number of weeks that Elvis' Blue Hawaii album stayed at #1 on the charts. (20)
B. Elvis' height measured in feet. (6 )
C. The day in August 1977 on which Elvis died. (16)
D. It was on this day in April of 1957 that Elvis moved in to Graceland. (10)
E. The number of times that Elvis was nominated for a Grammy Award. (14)
F. The number of Elvis' top 40 hits that hit #1 (he had 107 top 40 hits). (18)
G. The day in May 1960 of Elvis' television special, "Welcome Home, Elvis." (12)
H. Elvis' age when he moved into Graceland. (22)
I. The day in January 1935 on which Elvis was born. (8)

Perfect answer, way to go brainy! Ask in reception for your goodie bag.



The A to K Toys R Them has a number of bikes, tricycles, and wagons left over Christmas stock.

There is an equal number of trikes and wagons left, and there is a total of 60 pedals and 180 wheels.

How many wagons, trikes, and bikes are there


If you can't ride:

There is a common English word that is nine letters long. Each time you remove a letter from it, it still remains an English word - from nine letters right down to a single letter.

What is the original word, and what are the words that it becomes after removing one letter at a time

The common english word is : Startling

Remove the l, and it becomes: starting
Remove the t, and it becomes: staring
Remove the a, and it becomes: string
Remove the r, and it becomes: sting
Remove the other t, and it becomes: sing
Remove the g, and it becomes: sin
Remove the s, and it becomes: in
Remove the n, and it becomes: I

[size=8]BIKES, TRIKES, AND WAGONS
bikes: 6
trikes: 24
wagons: 24[/size]

What is the only word in the English language that when capitalized is changed from a noun or a verb to a nationality : Polish

lighthouse:1.4miles

distance from top of lighthouse to horizon:
92ft: sqrt((4000x5280+92)^2-(4000x5280)^2)=62338.50ft
72ft: sqrt((4000x5280+72)^2-(4000x5280)^2)=55147.85ft

distance from base of lighthouse to horizon following curvature of earth:
92ft: tan^-1[62338.50/(4000x5280)]/(2pi) x 2pi4000 = 11.8mi
72ft: tan^-1[55147.85/(4000x5280)]/(2pi) x 2pi4000 = 10.4mi

difference: 1.4 miles

[size=8]LIGHTHOUSE
line of sight to surface of the water (tangent):
10.44467 miles vs. 11.80653 miles (difference = 1.36187 miles)

along the surface of the water (earth's curvature)
10.44464 miles vs. 11.80650 miles (difference = 1.36186 miles)

Of course, it could be seen by a ship of non-zero height at a greater distance.[/size]

I'm off to Oregon for the holiday. My participation will be spotty for the next week. Happy Holidays to all.

The letter "E" surprise surprise

[size=8]DOVES
4 doves
3 cages[/size]

Name 10 Body Parts-no profane words-with 3 letters each


In almost every language, this word begins with the 'm' sound


What word or expression is represented below
GIVE, GIVE, GIVE, GIVE, GET, GET, GET, GET

ear, eye, toe, leg, lip, hip, arm, etc.
mother
forgive and forget