NeoPets Riddles (Lenny Conundrums) and Answers Here

I'm new
I'm new here, but I agree with Roly_Poly_Sandwiches on this one. Logic thinking. "Suppose you have a Kacheekers board with tan and grey squares, each square measuring 5 cm by 5 cm.

What's the largest circle that can be drawn on the board such that the entire circumference of the circle is only touching grey?"

Read into it, it wants to know how big a circle can be if only the circumference (i.e whole entire circle) is ONLY TOUCHING GREY. There can not be any tan in the middle of it if the circumference can only touch grey. The answer is "1 square" or "5 cm by 5 cm"

Anybody agree with that explanation?

That makes sense, except I was always taught the circumference of a circle was the outside edge. The entire circle would be the area....

am I right?

i think the answer to this problem is 15.70. If you only draw a circle around 1 of the gray squares, the diameter would be 5.

5xpi(3.14)+15.70.

Thats the way you find the circumference. You take the radius, multiply is by 2, and the take the answer, which is the diameter, and multiply it by pi, or 3.14!

x2silk2x, I think your right! right you can only draw a circle around one of the grey squares wich is 5 and 5 x pi=15.70 :wink:

?!?
Hey guys, how do we submit the answe?I mean in what form (Circumference or 'd' or 'r').

Ok I can see your reasoning about a formula. And I think I was wrong in saying the circumference is the whole circle. But in the question it does not say you had to find the circumference "What's the largest circle"

Anyways, I already submitted 5 cm by 5 cm.

If one were to choose the circle as indicated previously, the radius of the circle would 7.90569415042 if I did my math right.

From the center grey square we can make a triangle whose hypotenuse meets the corners of the two adjacent grey squares. The two sides would be7.5cm and 2.5 cm. The radius of the circle would be r sq = 7.5 sq + 2.5 sq. r = 7.90569415042. This would negate the need to find the small area in the partial grey squares.

they want to know the radius of the circle not the circumfrence or dimensions of it....

What's the radius of the largest circle that can be drawn on the board such that the entire circumference of the circle is only touching grey? Please round to the nearest hundredth of a centimeter

so i put 2.5cm as my answer.

What's the radius of the largest circle that can be drawn on the board such that the entire circumference of the circle is only touching grey? Please round to the nearest hundredth of a centimeter

They've updated the problem! It's not fair!

But, 1 square can't be right... If it is a grey square, the circle touches a white one, always! So, the radius must be more dan 2,5...

I'm sorry, but they updated it without me knowing as well. Which is not fair as someone already said, Are we able to submit an answer now since they updated it?

i wrote the FAQ section about it here is what I wrote

You changed the Lenny Conundrum after I have already submitted my first answer that did not say we needed it to be in measurements. 1st conundrum said "Suppose you have a Kacheekers board with tan and grey squares, each square measuring 5 cm by 5 cm.

What's the largest circle that can be drawn on the board such that the entire circumference of the circle is only touching grey?"

It was changed to "Suppose you have a Kacheekers board with tan and grey squares, each square measuring 5 cm by 5 cm.

What's the radius of the largest circle that can be drawn on the board such that the entire circumference of the circle is only touching grey? Please round to the nearest hundredth of a centimeter"

I would like the chance to submit a different answer due to the fact that you changed it on thursday night after some people have submitted their answers on Wednesday night. It's just not fair to other players and it won't let me submit a new answer.

with the pics in the previous posts, i see the circle as 'touching' the tan squares on the corners.

wrong that neopets changed the question... hope they accept answers if they would have the correct radius

the picture is not accurate of course, it's hard to use paint to make a perfect circle but if you think about it, it is correct, just resize a little bit of the bottom and such so that it fits perfectly. I have done it and I do have the answer. My boyfriend helped me on this one. I tried to submit my answer again, but it would not let me. I wrote to one of the TNT staff members too.

If you are completely stuck, e-mail me at [email protected]

I do have the answer, but I will not post it out here, for there are lurkers that come on this board even if they are not registered, they can still read it. How do you think I found out about it. But I want to help out too. That's why I signed up.

i used to be one of the 'lurkers' cuz i never could get on in time to help contribute to finding the answer. kinda cool tho when u do help solve the problem.

The answer is 7.91 (half of 5*sqrt(10)).

We have an eight-by-eight board, with squares alternating in color between tan and grey. For this exercise to work, we must assume our circle to be "ideal"; that is, the line drawing the circle has no width. (This is not realiistic, of course, but is fine mathematically.)

The circle cannot go outside the board, so it cannot fully include any of the squares along the edge of the board. To pass between grey squares, the circle must pass through the corners of the squares. Let's check cases:

If the circle is centered on a tan square and includes fully only that square, then the circle would pass through the corners of that square and through the interiors of the four surrounding grey squares. The radius would be (2.5)(sqrt[2]), by basic right triangles.

Can the circle be centered on a grey square and include fully the four surrounding tan squares? If so, then the circle must pass through the far corners of those tan squares. Does it? We can check by confirming that the distance from the center of the central grey square to those corners is always the same (this distance being the circle's radius). Drawing right triangles, it may be shown that these distances are (5/2)(sqrt[10]). So this circle will work.

Continuing outwards, can the circle be centered on a tan square and include fully the four surrounding grey squares and the eight tan squares in the next "layer"? If so, then the circle must pass through the far corners of those tan squares. The distance from the center of this grouping of squares to, say, the top right corner of the first tan square to the right of the central square may be shown to be (5/2)(sqrt[26]). But the distance from the center to the top right corner of the tan square one up from this square may be shown to be (15/2)(sqrt[2]). So this circle won't work.

The next circle would be centered on a grey square and would require the board to extend for four squares from each side of the central square. But the board is only eight-by-eight, so larger circles are not possible.

So the largest radius would be that of the second circle: (5/2)(sqrt[10]), or about 7.9056941504... centimeters. Rounded to the nearest hundredth, this is 7.91 cm.

Eliz.

I am trying to figure out where you got the equation ... (5/2)(sqrt[10])...
if it is to figure out the diagonal line from corner to corner of 1 square,(which would be the Diameter of the circle... then the equation should be...
A(squared) + B(squared) = C(squared)
or 5sq + 5sq =Csq ... 25 + 25 = Csquared or
the Diameter = square root of 50
so the Radius = 3.535 cm

Lenny Conundrum
Using the information about the Kacheekers board from last week's Lenny Conundrum...


What is the area of only the grey squares inside of the circle, in square millimetres? Please round to the nearest square millimetre.

new lenny
so if the circle was 7.91 cm then we convert to millimeters as there would only be 1 square right