You are correct, wcy.
Good, you didn't tell how you did it
Try earlier problems too.

Ganesh, I am thinking of an upgrade to the "hide" tag.

Wouldn't it be cool if we could really hide the results from everyone (except moderators) until a certain time, maybe 1 week after the post, or based on the time you post the question.

A third possibility would be for you to have a keyword in the topic like "open" and that could be what controls whether the hide tag really hides, so "Ganesh's Puzzles" would be a list of solved/unsolved puzzles, with other peoples answers hidden until you let them be shown.

I would obviously need to program all this, and I am not sure the hurdles I would face, but what do you think of the idea?

So, do you think it would be good to post a new topic for every puzzle? That way they could have titles like "Cut a Square (Current)", which you can edit to "Cut a Square" when it is solved. I could use the phrase "(Current)" to tell the forum to really hide answers in the hide tag.

Also, if someone posts a full answer you can edit their post, insert a "hide" tag and put a gentle reminder to use the hide tag

(This is all based on the assumption I can get the hide tag to work like we want!)

Problem # k + 12

In a 4-digit number, the sum of the first two digits is equal to that
of the last two digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other two digits. What is the third digit of the number?

Solution to problem # k + 9

The side of the square is 2.
Let a length 'c' be cut from the two ends of a side.
We have right angled triangles of sides 'c'.
The hypotenuse would be h² = 2c²
or h = (√2)c
Since it is a regular octagon.
2 - 2c =  (√2)c
c = 2/(2+√2)
h is the side of the octagon,
h = 2 (√2)/(2+√2)
or h = 2/(1+√2)

I guess 1/18 chance if they can't both be the same chess square.

Problem # k + 14

What is the area of the largest triangle that can be fitted into a rectangle of length 'l' units and width 'w' units?

Last edited by John E. Franklin (2005-09-05 12:42:33)

Good work, John E. Franklin 

Solution to Problem # k + 14

Any triangle you try to draw with the maximum area would have same base and height. The solution is, without doubt, lw/2. You can try all possibilities. You'd get the same answer, both when the base is 'l' and 'w'.

Solution to Problem # k + 12
Yes, you would be one equation short. But, when you get one number is eight times the other, the numbers would have to be 1 and 8, as each number a,b,c, and d is a single digit number!

Solution to Problem # k + 10
Yes, 5121 is the correct answer. As you said, there may not be another as 0242 is not acceptable!


Solution to Problem # k + 11
You have given a different property! I had this is my mind.
It is a number of the form abcd equal to (a^b)*(c^d)

Solution to Problem # k + 6
You are correct. The ages of the grandmother and the grandson would be (61,1), (62,2), (63,3), (64,4), (65,5), and (66,6).

Solution to Problem # k + 6

You are right, John. I don't know the reason. Just as MathsIsFun thought, I too believed 97531 x 86420 would be the highest product!

Problem # k + 16

The pages in a book are serially numbered from 1. If the number of digits required to total all the pages in the book is 972, how many pages are there in the book?

John, you went wrong somewhere; please try again