MathDB

p1. Determine all three-digit numbers

\overline{XYZ}

that meet the equality

\overline{XYZ} + \overline{YXZ} = \overline{WWZZ}

where each letter represents a digit, equal letters represent equal digits, and different letters represent different digits.
p2. A machine for numbering pages is ruined, the problem it has is that it does not print the numbers that are multiples of

3

nor those that are multiples of

5

. The numbering on the pages of a book is the following:

1, 2, 4, 7, 8, 11, ...

If the last issue printed in this book is

2012

, determine the number of pages in the book.
p3. Let

x, y, z

be three positive numbers that satisfy

x+\frac{1}{y}=\frac73

y+\frac{1}{z}=1

z+\frac{1}{x}=4

Determine the product

xyz

.
p4. Let

ABC

be a triangle right at

C

, draw the altitude

CD

. It is known that the area of the triangle

ADC

is one fourth part of the area of the triangle

ABC

. Determine the measures of the angles of triangle

ABC

p5. Determine for what value

n

it is possible to form with

9

people,

n

groups of

3

people each so that each pair of people is in exactly one group. Show one of the possible group configurations.

Problem Statement