MathDB

p1. Figures

0

1

2

and

3

consist of

1

5

13

and

25

squares. If you continue with this scheme, define how many squares figure

100

has. https://cdn.artofproblemsolving.com/attachments/2/1/ffc1675513e285e51881b6ef54aa5fb2640605.png
p2. The figure shows

5

scales with objects and the total weights in each of them: https://cdn.artofproblemsolving.com/attachments/d/5/4408d9f3ae40b5fcb4c5e30941b699bffd65ed.png One of the scales malfunctions and the other

4

indicate the correct weight. Determine which scale is malfunctioning and enter the weights of each object :

\blacklozenge

\bullet

\Box

p3. The positive real numbers

a

and

b

satisfy the relation

ab = a-b

. Find the value of

a/b + b/a - ab

.
p4. Let

ABCD

be a square of area

1

. Let

P

and

Q

be points outside the square such that the triangles

ABP

and

BCQ

are equilateral. Find the area of the triangle

PBQ

.
p5. Place different natural numbers greater than

1

in the boxes, so that each number is a multiple of the number written in the box to its left, and that the sum of the five numbers is

517

. https://cdn.artofproblemsolving.com/attachments/6/3/8257ecdaac09b73186e9c84b26668d5b26e413.png

Problem Statement