Wednesday, August 29, 2001

Round 23

Date released: August 29th, 2001.
Date rewarded: September 12th, 2001.

The Fontaine sisters are seamstresses by trade. They have been commissioned to create as many 2 by 3 feet rectangular Jolly Roger flags as they can for the pirates in their village, so Loretta Fontaine has gone out to buy cloth to embroider.

Dark cloth costs 150 Neopoints a foot and comes in a roll five feet wide. It can be bought in any length (even down to the inch). She has a total of 1,260 Neopoints to spend on the cloth.

How many WHOLE Jolly Roger flags will they be able to make???



Click to show/hide solution

Number of feet of the Dark cloth that the Fontaine sisters can buy:
1260 / 150 = 8.4 ft

The area of the bought cloth:
8.4 * 5 = 42 ft²

Number of possible whole flags with that area of the cloth:
42 / (2 * 3) = 7

However, if we check the below figure, the is no way to make 7 flags from the cloth (each flag must have 2 ft x 3 ft dimension). The sisters can make maximum 6 flags from the cloth.

Therefore, the Fontaine sisters can make 6 whole Jolly Roger flags.

Friday, August 17, 2001

2x Champion trophies

From TNT:
GREAT NEW FEATURE - We are now counting the number of times you come first in a variety of our games. If you win Mystery Pic twice you will be a 2x Champion instead of just a champion. The games that keep track of wins so far are Mystery Pic, Lenny Conundrum and Better Than You.
Good news for those who want to compete for the first place.

Tuesday, August 14, 2001

Round 22

Date released: August 14th, 2001.
Date rewarded: August 29th, 2001.

This week's Conundrum is harder than the rest, and requires you to use your knowledge of Neopets :)

To the nearest 100,000 - how many shops are there in Neopia?

Round your answer down to the nearest hundred thousand (ie.. if you guess at 445,038 then you would say 400,000).


Click to show/hide solution

This week puzzle is for guessing. If you are lucky, you guess it right. The right answer is 3,000,000.

Friday, August 10, 2001

Round 21

Date released: August 10th, 2001.
Date rewarded: August 14th, 2001.

'Excuse me, Slave', said Princess Vyssa, 'I have a job for you'. 'What is it?', Burlak groaned??? Princess Vyssa handed the sculptor a big ball of clay. 'I would like some decorations for my new palace. I want you to build me lots of little pyramids out of this clay. The base has to measure 8 centimeters by 8 centimeters, and they have to be 6 centimeters high..

Burlak looked at the ball of clay, and measured it. It's diameter was 20 centimeters, and it seemed to be a perfect sphere. He wondered how many pyramids he could make... do you know?


Click to show/hide solution

Volume of a pyramid [1]:
V1 = B * h /3 = 82 * 6 / 3 = 128 cm3

where B is the area of the base of the pyramid, h is the height of the pyramid.

Volume of the sphere [2]:
V2 = 4/3 * pi * r3 = 4/3 * pi * 103 = 4000/3 * pi cm3

where r is the radius of the sphere.

Total number of pyramids that Burlak can make:
N = V2 / V1 ~ 32.72

Therefore, he can make 32 pyramids from the clay sphere.

[1] Pyramid volume
[2] Sphere volume

Thursday, August 2, 2001

Round 20

Date released: August 2nd, 2001.
Date rewarded: August 10th, 2001.

The economy of Roo Island is rather strange. They have four coins, each worth a different number of Neopoints. Three red coins plus two Neopoints equal a green coin. Three green coins plus five Neopoints equal a purple coin. Eleven red coins plus a single Neopoint equal a purple coin.

The fourth coin is a silver coin that is worth four purple coins. If I go to the Roo Island bakery and buy a loaf of bread worth 84 Neopoints with my silver coin, and the shopkeeper gives me change in red coins... how many red coins would I get?


Click to show/hide solution

Let r, g, p, s be the values of red, green, purple and silver coins respectively. We know that:

* Three red coins plus two Neopoints equal a green coin:
3r + 2 = g (1)

* Three green coins plus five Neopoints equal a purple coin:
3g + 5 = p (2)

* Eleven red coins plus a single Neopoint equal a purple coin:
11r + 1 = p (3)

* Silver coin is worth four purple coins:
s = 4p (4)

From (2) and (3), we have:
3g + 5 = 11r + 1 <=> 11r = 3g + 4 (5)

From (1) and (5), we have:
11r = 3g + 4 = 3 * (3r + 2) + 4 = 9r + 10 <=> 2r = 10 <=> r = 5

g = 3r + 2 = 17
p = 3g + 5 = 56
s = 4p = 224

The change that I should get (in red coins):
change = (224 - 84) / 5 = 140 / 5 = 28

I should get back 28 red coins.