bonanova

Nice analysis wolfgang!

but these are 9 digits and not 8 , so you should devide the number by 9. You're right of course. I meant to point out that 96325814 / 8 = 12040726.75

Nice!

Yah, you got it. Here's basically just a different wording:

Sooooo close. Swap a single digit from each number and you have it.

Very close, wolfgang, but check out the first eight digits.

This time there are all ten digits: 0 1 2 3 4 5 6 7 8 9 I just made a single number, using each of them exactly once: like 4623901875. Can you guess my number? Of course you need some clues: (and we'll see whether 4623901875 fits.) The number formed by the first digit (4) is divisible by 1 - OK two digits (46) is divisible by 2 - OK three digits (462) is divisible by 3 - so far, so good ... four digits (4623) is divisible by 4 - Oops ...guess not. five digits is divisible by 5 six digits is divisible by 6 seven digits is divisible by 7 eight digits is divisible by 8 nine digits is divisible by 9 ten digits (the entire number) is divisible by 10 - Aha! The last digit is zero. And digit 5 must be ...

Kewl - can't wait to play this one - if only to understand the roles.

Here are your digits: 1 2 3 4 5 6 7 8 9. Using each of them exactly once, form two numbers: for example, 314879 and 652. What's the largest product two such numbers can have?

Very close.

How many square meters?

What's the triangle's area? The idea behind the puzzle question makes it an easy calculation.

On the right track.

An ellipse is 1 meter wide at its narrowest point and four times that amount at its widest point. A triangle is drawn using three points on the ellipse. How large can it be?

What friends / past players can we lure into this game?

Thanks for the analysis. Beginner's misktake - I gained nothing from misleading since I was a goodie. Still learning and getting hooked while doing so.

Wondering if the "moves from A to B" calculation could be put into an Excel macro to paste into the cells of a 255x255 Excel array. Just thinking. Or maybe there's an Aha! Solution... Wolfgang's answer answer has merit.

Who else is in?

Agree. What it seems to boil down to is constructing a 255 x 255 matrix, looking for the smallest number in each column and selecting the row having the largest minimum, for the second answer, and the column through the smallest maximum for the first part. That's a lot of computing, once an algorithm is found to get from any A to any B in the fewest moves.

Agree with JIntorcio. The restriction that x is not 1 mile is innocuous, since that value has no inferable relation to the length of the track. A standard approach with an unspecified parameter is to assign it a value, say 10 in this case, inferring that the answer does not depend on the value. (else it would be given.) Best example of this is the hole-in-the-sphere problem.

The other night I wrote down a number. I thought about ways to turn it into a palindrome. I tried adding it to the larger number I got by reversing its digits. That didn't work. But I kept on doing that step, using each time the number I got from the previous step. Whether this process will always produce a palindrome, eventually, I don't know. But for my starting number it eventually worked. Can you tell me my starting number? I can tell you that after the second step the number of digits had not increased, and that a four-digit palindrome was the first to appear, after the fourth step.