The worlds first riddle!

NUMBERS
I get 3771 solutions ignoring rearrangements.

Yes Try I would like to stick with answer:

Quarter and 5 cents - so, one is not a quarter

The sum of the digits of an even number is 95
the sum of the digits of half the above number
70. How many odd digits has this number?


Whim

Merlin:

Legs:
"6060"

Damn, I thought that would run and run.

Geographical Position.
Nope. It's below Africa's western lobe.


If your latitude is 0°, you must be somewhere on the equator, the line separating the northern and southern hemispheres. If your longitude is 0°, you are standing on a line that connects the North and South Poles, and passes through Greenwich, England. The two lines meet in the Atlantic Ocean, a few hundred kilometres south of Ghana and west of Gabon.


Mark makes a good point, "Are you sure the mathematician didn't intend for all solutions to be counted?"


No I am not. I was just going from the wording, ""876+429 = 1305 is one way to write a sum which uses all digits (0-9) only once."

Then, "The same question may be asked for products."

Which is one of the reasons I mentioned the (two-digit) answer. A better answer would be ALL possible combinations. I turn the page and you )have again) beaten me to it.

NUMBERS
Mark:
"I get 3771 solutions ignoring rearrangements." Very

I don't think I could get anywhere near that number. Well done.


VOWELS
"Five Thousand"


Thinking I would be able to get MyO to change his mind, he replied, "Yes Try I would like to stick with answer:

"Quarter and 5 cents - so, one is not a quarter"

Good answer!


Whim, your puzzle looks testing (as always)




How many times can a student stuff an unknown number of books into an large empty book bag


If all the numbers in existence starting with zero were written in English and then arranged in alphabetical order, what number would be first



What is the only English word for a number that when spelled, its letters are in alphabetical order



Time for breakfast, follow these instructions: Take one full cup of coffee and drink 1/6 of it. Replace what you drank with milk. Now, drink 1/3 of the coffee/milk mixture. Again, replace what you drank with more milk. Now, drink 1/2 of what is in the cup. Once again, replace what you drank with milk. Now drink the entire cup of mixed coffee/milk.

The questions are:
Have you had more milk or more coffee
How much of each have you had

More coffee; you've added less than a cup of milk.

BOOKS
Once. After that, it's not empty.

FIRST ALPHABETICALLY
Is this limited to integers?
8 unless 1,000,000,000 is written 'billion' instead of 'one billion'

If not limited to integers, how about 6.022x10^23 (Avogadro's number)?

LETTERS IN ALPHABETICAL ORDER
forty

COFFEE
1 cup of each

1/6 + 1/3 + 1/2 = 1

One solution:
Five odd digits
649898989898
324949494949

Whim

Merlin, it's all about ?'having a go' and a bit of a laugh. As Mark pointed out, jest look at Havagoe's number: 6.022x10^23. Now that is what I call a number.


Mark
BOOKS
Once. After that, it's not empty.

FIRST ALPHABETICALLY
Is this limited to integers? YES
8 unless 1,000,000,000 is written 'billion' instead of 'one billion' :wink:


LETTERS IN ALPHABETICAL ORDER
forty

COFFEE
1 cup of each

If I may be so bold to comment on:

One solution:
Five odd digits
649898989898
324949494949

Utterly amazing.




A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, the second is full of assassins with loaded guns, and the third is full of lions that haven't eaten in 3 years. Which room is safest for him


What letter is next in this sequence

F F S S E ?


What is the smallest number which when divided by 10 leaves a remainder of 9, when divided by 9 leaves a remainder of 8, when divided by 8 leaves a remainder of 7, when divided by 7 leaves a remainder of 6, and so on until when divided by 2 leaves a remainder of 1

I suppose one with lions, because if they haven't ate for 3 years, they must be dead

Next Letter:
N (then T, then E, then T)

REMAINDERS
2519 (LCM of 2-10 minus 1)

MyO
"I suppose one with lions, because if they haven't ate for 3 years, they must be dead."

You suppose right.

Merlin
Next Letter:
"N (then T, then E, then T)" Ok, ok. You still only get one point.

Mark
REMAINDERS
"2519 (LCM of 2-10 minus 1)" Nice one.


Don't blame me, blame Whim.


Can the number ?'2000' be made from 8 different digits in increasing order (without using concatenation) If so please give one or two examples.


Now, let us explore writing numbers with copies of one digit.
For example, a persons age could be written as (1+1+1)11+1, 2*(22+2)+2, 33+(3/3), 4*(4+4)+(4+4)/4, 5*5+5+5-(5/5), 6*6-(6+6)/6, 7*7-7-7-(7/7), 8+8+8+8+(8+8)/8, or 9+9+9+9-(9+9)/9.

Question: How old is that person

Therefore, what is the shortest way to make 2000 using copies of one digit each of (1-9)

(1-(2+(3+4))) * (5 * (6-(7 * 8 ))) = 2000
2-(((3/4) * (5-(6 * 7))) * (8 * 9)) = 2000



Question: How old is that person? 34



Whim

Blame Whim for what?

2*(22+2)+2 = 50, not 34

2000 NINE WAYS
I don't claim that these are optimal. I'm using the underscore to represent the bar that is placed over a digit to the right of the decimal point to indicate infinite repetition. Holler if any of the operations I use are illegal.
(1+1)/(.1^(1+1+1)) (6 ones)
2*(2/.2)^(2+2/2) (6 twos)
(3-3/3)*(3/.3)^3 (6 threes)
sqrt(4)*(4/.4)^(4-4/4) (6 fours)
.5*(5!+5)/(.5)^5 (5 fives)
sqrt(((6/.6)^6)*6*.6) (5 sixes)
((7+7)/7)*(7/.7)^sqrt(7/.7) (7 sevens)
(8+8)*8*8/(.8*.8*.8) (7 eights)
(.9+.9)*(9/.9)^sqrt(9) (5 nines)

Whim gets off to a flying start.
(1-(2+(3+4))) * (5 * (6-(7 * 8 ))) = 2000
2-(((3/4) * (5-(6 * 7))) * (8 * 9)) = 2000

Are there any more? Yes of cause there are.


Blame Whim for what? Repeating digits. Oh. and the poor weather. :wink:

2*(22+2)+2 = 50, not 34. Any further advances?

Mark:
"2000 NINE WAYS"

Mark sets the standard to go for. BTW there are at least nine ways using 3's. Any other takers?



Holler if any of the operations I use are illegal.

?'I am sorry to hear that. I once had a sick parrot, but an ill eagle is another matter.'

None could do better.

(1+1)/(.1^(1+1+1)) (6 ones)
2*(2/.2)^(2+2/2) (6 twos)
(3-3/3)*(3/.3)^3 (6 threes)
sqrt(4)*(4/.4)^(4-4/4) (6 fours)
.5*(5!+5)/(.5)^5 (5 fives)
sqrt(((6/.6)^6)*6*.6) (5 sixes)
((7+7)/7)*(7/.7)^sqrt(7/.7) (7 sevens)
(8+8)*8*8/(.8*.8*.8) (7 eights)
(.9+.9)*(9/.9)^sqrt(9) (5 nines)



Perhaps someone would be kind enough to help me out. My problem is, I have a number of calculations to make, and my calculator will only print out ?'9's. Can you think of a way I can only use ?'9's to make copies of the digits 1-20

As the battery is low, can you please do so in the shortest way. Thank you.


It is known that the first 144 digits of Pi equals 666. The first 146 digits of the golden ratio equals 666.

Given a random irrational number, what is the probability that 666 will be hit exactly by taking successive digits


You are presented with 3 envelopes. Each envelope has 2 statements written on it, the statements on one envelope are both true, the statements on another are both false, and the remaining envelope has one statement that is true and one that is false.

Envelope 1:
1. The formula is not in here
2. The formula is in envelope 2

Envelope 2:
1. The formula is not in envelope 1
2. The formula is in envelope 3

Envelope 3.
1. The formula is not here
2. The formula is in envelope 1.

Which envelope contains the formula

Envelope 3

CALCULATOR
No claims that these are optimal. The underscore is again used as the repetend bar.
1 = .9
2 = .9+.9
3 = sqrt(9)
4 = sqrt(9)+.9
5 = sqrt(9)!-.9
6 = sqrt(9)!
7 = sqrt(9)!+.9
8 = 9-.9
9 = 9
10 = 9/.9
11 = 9/.9+.9
12 = 9 + sqrt(9)
13 = 9/.9+sqrt(9)
14 = 9+sqrt(9)!-.9
15 = 9+sqrt(9)!
16 = 9/.9+sqrt(9)!
17 = 9+9-.9
18 = 9+9
19 = 9/.9+9
20 = (9+9)/.9


IRRATIONAL
1/5 (based on simulations)