Problem of the month

PROBLEM

Find how many couples of integers satisfie at the same time these two conditions:

the sum of their squares is minor than 13;

the sum of their absolute values is major or equal to 4.

Can we change the number 13 in order to have exactly four couples of integers?

solution by: Anna Barisan and Gioella Lorenzon

PROBLEM

A rope which length is l meters is bonded to the ceiling trough one of its endings. The other ending is pulled up vertically in a way for the rope to be disposed as in the figure. If the free ending is pulled up of n meters, how much does the lowest point of the rope ascend? Suppose that segments AB and BC, whose sum is obviously l, are perfectly parallel.

solution by: Teacher carraro

PROBLEM

Rewrite the following polynomials as squares:

x⁴ + 6x³ + 17x² + 24x + 16;

x⁴- 8x³ + 26x² - 40x + 24.

solution by: razvan galatanu
solution by: teacher fabio breda

Archimede project site made by:
Razvan Galatanu, Andrea Pizzardo, Leonardo Rebeschini, Pietro Zanin e Luigi Maninchedda.

Archimede Project