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

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

days 120 times

race 13 cars

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).