I don't know if you know these, I don't even think they exist outside of Italy, but Archimede's Maths Games are a maths&logic "contest" that takes place every year in Italy's schools. I wanted to share with you the 20 questions that I had to answer, obviously translated in English. No calculators should be allowed. Here we go:
Mark gives 1260 stickers to all of his friends, that are less than 100, giving each of them the same number of stickers and giving them all. What's the maximum number of friends Mark can have? (A: 70; B: 84; c: 90; D: 94; E: none of these)
Given the rectangle in the picture gets divided by the line in two parts, whose surfaces are one 4 times bigger than the other, calculate the ratio between the length of A and B. (A: 2/3; B: 1/4; C: 1/5; D: 1/2; E: 2/5)
On the planet Papalla (please don't ask) an year is made of 400 days, numbered from 1 to 400; days whose number is a multiple of 6 are holiday. The new Papalla's government renews the calendar, dividing the year in 10 months of 40 days each, numbered from 1 to 40, and the prevoius holiday rule still applies. After the change, the number of holidays in an year (A: is still the same; B: has increased by less than 10%; C: has increased by 10%; D: has decreased by less than 10%; E: has decreased by 10%)
S1 and S2 are two spheres; S2's volume is two times S1's volume. What's the ratio between S2's surface and S1's? (aA cubic root of 4; B: 2; C: 2 times cubic root of 2; D: sqrt(8); E: none of these)
Matthew, to reach his school, has to go 2km uphill, and manages to get there in 12 mins. When he goes back home, it only takes 4 minutes. What's the average speed in the whole path? (A: 10KM/h; B: 12KM/h; C: 15KM/h; D: 20KM/h; E: none of these)
The triangle in the picture (AC == AB, I don't remember the correct word) has AB 1m long and CH 2m long. The square inside it has a vertice in H, and two vertices on AC and AB: find the square's surface. (A: 1/5m^2; B: 5/16m^2; C: 8/25m^2; D: 1/3m^2; E: 1/2m^2)
In a class the blonde people are the 40%, while the others have brown hair. Of the blonde people, 75% are girls. Given that, in the class, the number of girls equals the number of boys, what's the percent of boys with brown hair in the class? (A: 20%; B: 25%; C: 30%; D: 40%; E: 50%)
A floor is tiled, as in the picture. How many ways to color the tiles can you find, given that you can use only blue, red and black and two touching tiles can't be the same color? (A: 0; B: 2; C: 3; D: 6; E: endless)
How many couples of prime numbers can you find that make (p^q)+1 still a prime number? (1 is not a prime number) (A: 0; B: 1; C: 2; D: endless; E: none of these)
In 22nd November 2012, 35% of petrol's price is its actual cost, whose 24% is oil/petroleum's cost. Given that the first of December 2012 oil's price will increase by 10% and the other costs stay as they are, how muchw will petrol's price increase by? (A: 10%; B: 2.4%; C: 3.5%; D: 0.84%; E: none of these)
Find the sum of the figures in (10^2012+1)^3. (A: 4; B: 8; C: 2012; D: 2013; E: none of these)
Which of the following numbers is the greatest number that always divides n^5-5*n^3+4n, given that n is a natural number equal or higher than 3? (A: 15; B: 35; C: 60; D: 120; E: 240)
Which of the following is less than or equal to 1/6+x^2 for every real number X? (A: sqrt(1/6 + x^2); B: -(2/sqrt(3))*x; C: (1/6 + x)^2; D: 1/6+x; E: none of these)
Merlin (again, please don't ask) puts his hat on the ground, a cone of height = 20*sqrt(2) cm and base radius = 10cm. An ant, starting by a point P on the hat's edge, walks to the point Q, on the middle of the opposite apothem (see the picture). How much is the shortest possible path long? (A: 15*sqrt(3)cm; B: 15+10*sqrt(2) cm; C: 15+5*math.pi cm; D: 15+10*math.pi; E: none of these)
We've got a 4-sided die with the numbers 1, 3, 5 and 7 and an 8-sided die with the numbers 2, 4, 6, 8, 10, 12, 14 and 16. How is it likely to obtain two number whose sum is 11 with just one roll? (A: 1/16; B: 1/8; C: 1/4; D: 1/2; E: 1)
Given that K is an integer and that x^10+k*x^2+4=0 has at least one solution (an integer), how many different values can K have? (A: 1; B: 2; C: 3; D: 4; E: endless)
Given a two-figures number which is a perfect square (16, 25, 36, 49, 64, 81), how is it likely to get a multiple of 11 by adding a random figure between 1 and 9 to the left of the number? (A: 1/9; B: 2/9; C: 3/9; D: 4/9; E: depends on the number)
Carl has 6 apples and 6 pears: how many ways can he put 6 fruits in a row in, given that he can't put a pear between 2 apples? (A: 16; B: 22; C: 32; D: 35; E: 39)
A grasshopper moves by jumping exactly 10 cm. It moves by jumping a certain amount of times in a direction, then it rotates by 120° towards its left and jumps twice the previous times. Then it rotates by 120° towards it left again, and so on. Given that it starts by jumping just one time towards a given direction, how much will it be distant from the start after 17 jumps? (A: 20cm; B: 20*sqrt(3)cm; C: 40cm; D: 40*sqrt(3)cm; E: 50cm)
X is a float number higher than 1. (x-1)((x+1)^2012) equals 1. X is: (A: 1 < x < 1+1/(3^2012); B: 1+1/(3^2012) < x < 1+1/(2^2012); C: 1+1/(2^2012) < x < 1+1/3; D: 1+1/3 < x < 1+1/2; E: x > 2)
The picture:
lf = love.filesystem
ls = love.sound
la = love.audio
lp = love.physics
lt = love.thread
li = love.image
lg = love.graphics
!