The worlds first riddle!

Well, you got the number right.

Now all you need is the unit of measurement....

ADRIAN
12 miles

It takes him 16 minutes on Monday and 18 minutes on Tuesday.

usamashaker: He drives 40 and 45 miles per hour, not per minute.

PRODIGITIOUS
The answer is at most 22.
A digit other than zero and one cannot appear in consecutive numbers because the products for both numbers would be divisible by that digit, but at most one of the two numbers could be divisible by that digit. Therefore, the longest possible consecutive sequence looks like this:
XXX...XY99
...
XXX...XZ20
where the X's are zeros or ones (or nines in the first number), Y is nine or zero, and Z is zero or one (based on the value of Y).

Please don't publish the answer yet, as I'd like to give this more thought.

PRODIGITIOUS
Update:
The answer is 13. This is where Try's hint comes into play.

The numbers that end in 3, 6, or 9, will have P(N) equal to 3, 6, or 9 (all other digits are 0 or 1). Therefore, the number of ones in the numbers must be a multiple of 9 for P(N) to divide N when the number ends in a 9. The last two digits of the 13 numbers must be:
00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 10, 11, 12
with a multiple of nine ones in the digits preceding these.
If we try to extend the sequence at the beginning (x99), the number of ones will be one less, so x99 and x09 can't both be multiples of nine. If we try to extend the sequence at the end (x13), the number of ones will be one more, so x03 and x13 can't both be multiples of three.

If the hundreds place is set to zero, and there are a multiple of nine ones in the first number (sequence is x000, x001, ...), then P(N) is guaranteed to divide N for all N except x007. Just need to find such a number that is a multiple of seven.
1111011111007 is such a number.

Solution is:
1111011111000
1111011111001
1111011111002
1111011111003
1111011111004
1111011111005
1111011111006
1111011111007
1111011111008
1111011111009
1111011111010
1111011111011
1111011111012

Hi Usamashake. what a great start:

fork=4
spoon=4
knife=8
plate=12

135 tiles


Also a big high too And rian: :wink:

"Well, you got the number right."

Mark clears the fog of confusion with:
12 miles


Special mention: Mark's answer.

PRODIGITIOUS
Update:
The answer is 13.

You are in line for an ?'Emmy'


Stock answer:
Note that if any number n in our sequence ends in a 3, this implies 3 divides n. However, then n+10 also ends in a 3, yet is clearly not divisible by 3 (since 3 does not divide 10). The same trick works for numbers ending in 6 and 9, thus you can only have one of each in any consecutive sequence with the desired property. It follows that any such sequence has length at most 13, and indeed that it must go *0, *1, ..., *9, %0, %1, %2. Since I told you the answer was not 12, it has to be 13!
Consider sequences of the form (1)^n 000, (1)^n 001, ..., (1)^n 012, where for example (1)^3 000 = 111000. The freebies are the numbers ending in 00, 01, 02, 04, 05, 08, 10, 11, and 12. Let n be a multiple of 9, say 9*m; this gives us 03, 06, and 09 by the old trick of a number is divisible by 3 (9) if and only if the sum of its digits is divisible by 3 (9). The last number left is 07; we need that (10^{9m}-1)/9 is divisible by 7. This happens only if 10^{9m} = 1 (mod 7); by Fermat's little theorem this is ensured if 9*m is a multiple of 6 (and indeed, 10 is a primitive root modulo 7, so this is required). Let m=2k, then, so n=18k.
So we're done, the answer is 13, and one such sequence runs from 111,111,111,111,111,111,000 to 111,111,111,111,111,111,012.



The three of us made some bets:

• First, Waldo won from Molly as much as Waldo had originally.

• Next, Molly won from Spike as much as Molly then had left.

• Finally, Spike won from Waldo as much as Spike then had left.

• We ended up having equal amounts of money.

• I started with 50 cents.

Who am I


I wish to share thirty identical individual sausages equally among eighteen people. What is the minimum number of cuts that I need to make


An insurance company finds that it takes five clerks 17 days to process 2975 claims. How many clerks should be assigned to process 7595 claims in seven days


For years now, the famous Baron Munchhausen has gone to a lake every morning to hunt ducks. Since August 1, 1999, he's been saying to his cook every day, "Today I shot more ducks than two days ago, but fewer than a week ago."

What is the greatest number of days he can make this statement, taking into account that the Baron never lies

BETS
Molly

SAUSAGE
I believe 12 sausages need to be cut. I suppose that could be done in one stroke.

CLAIMS
31

7 DAYS?

oooooooh

false

it's 5 days

Mark:
BETS
Molly

SAUSAGE
I believe 12 sausages need to be cut.

CLAIMS
31


Usamashaker:

7 DAYS?


Clever idea, use all the days over the last few years. I think statistically the first answer you give has the highest probability of being correct.



This is an old fairground game, but can you calculate the mathematical chances of winning with a single go

To win, you must toss a 1 inch diameter coin onto a chequered board comprising 2 inch diameter squares; the coin must come to rest entirely inside a square, not overlapping any other square.



The boss planned to distribute fifty dollars of a bonus fund to each employee, but the last employee would have gotten only forty-five dollars. To effect an equitable distribution, forty-five dollars was given to each employee and ninety-five dollars was kept in the fund for the following year.

How much money was in the fund to begin with


A man calculated that if he skis 10 mph, he will arrive at his cabin in the woods at 1:00 pm. If he skis at a rate of 15 mph, he will arrive at the cabin at 11:00 am.

How fast must he ski to arrive at the cabin at noon

DUCKS
I get 6 days with these numbers:

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

He can start making the claim when he shoots 6 and end when he shoots 4.

DUCKS
What does the 7 day solution look like?

ski...... 12 mph

boss............. 995 dollars

ducks ?????????????

For years now, the famous Baron Munchhausen has gone to a lake every morning to hunt ducks. Since August 1, 1999, he's been saying to his cook every day, "Today I shot more ducks than two days ago, but fewer than a week ago."

What is the greatest number of days he can make this statement, taking into account that the Baron never lies"

What is the example solution for 7 days?

FAIRGROUND GAME
1/4

Usamashaker :
ski...... 12 mph

boss............. 995 dollars

Mark:
DUCKS
I get 6 days with these numbers:
9 9 9 9 9 9 9 5 1 6 2 7 3 8 4
He can start making the claim when he shoots 6 and end when he shoots 4.

"What does the 7 day solution look like?"

A very good question. When this problem was sent to me some time ago (I can not remember my answer) but was told it was wrong and that the answer is, ?'7 days'

Although I must say, your answer looks more reliable.

FAIRGROUND GAME
1/4

Fairground chequers maths puzzle: The calculation is very simple - the centre of the coin can be no closer to the edge of a square than half an inch. The 'win-zone' is therefore a 1 x 1 inch square defined by a half inch border inside each 2 inch square. The total area of each chequered square is 2 x 2 = 4 square inches; the win-zone in each is 1 x 1 = 1 square inch; so the chances of winning are exactly 1 in 4, or 25%, or 3 to 1 against.




Use only ONE of these symbols (+ - × ÷) to complete the formula:
10 10 10 = 9.50


Five friends met every week for a card game. They used a table with five chairs. Eventually, they realized that they had chosen a different seating arrangement each week and had exhausted every possibility.

How long had the friends played cards together


At a race track, one spectator watched a number of cars whirling around a circular track and said, "There's Bess, that woman in the white car!" Someone replied, "Yes, I see, but how many cars are running in this race?" Someone answered, "One-third of the cars in front of Bess added to the three-quarters of the cars behind her will give you the answer."

How many cars were being driven in the race

days 120 times

race 13 cars

Usamashaker:
days 120 times

race 13 cars


Tom gave four-fifths of his pencils to Sue, then he gave two-thirds of the remaining pencils to Ben. If he ended up with ten pencils for himself. With how many did he start


An oak rocking chair once owned by former President John F. Kennedy was sold in an auction for $442,500. This represents 8850% of its estimated value before the auction.

How many dollars was the estimated pre-auction value


The sum of three numbers is 98. The ratio of the first number to the second is 2:3, and the ratio of the second to the third is 5:8. What is the second number


What is 42 feet up in the air when it ?'kicked the bucket' and yet is still touching the ground

What happens if you add five nines at the front of your series and then continue it? (i.e., make the "6" land on a Sunday.)

DrewDad:
I don't follow. I made no assumptions about the day of the week. My approach was to find a sequence S(N), such that S(N-2)<S(N)<S(N-7).

PENCILS
150

CHAIR
$5000

NUMBERS
30


"Use only ONE of these symbols (+ - ?- ÷) to complete the formula:
10 10 10 = 9.50"

Use one once, or use one any number of times?