Questions from Young Mathematician Olympiad, 2017-2018, Stage A, Grades 5-6

Question 1 - Signs

A cyclist is riding on a straight road without turns and sees the following sign by the side of the road:

He continues moving and sees another sign:

Find the distance between cities B and C.

Arithmetic Algebra -> Word Problems

Additional sources:

Young Mathematician Olympiad, 2017-2018, Stage A, Grades 3-4 Question 1

Question 2

By what factor is the sum of all numbers from 1 to 99 smaller than the sum of all numbers from 1 to 9999?

Algebra -> Sequences -> Arithmetic Progression / Arithmetic Sequence

Grandma Hannah has many flowerpots with flowers in her house. One day, her three grandchildren, Avi, Beni, and Gili, came to visit and tried to guess how many flowerpots she has.
Avi said: "Grandma has more than 8 flowerpots,"
Beni said: "More than 10, I think,"
And then Gili said: "Grandma Hannah has at least 12 flowerpots."
"Two of you are right, and one of you is wrong," answered the grandmother. So how many flowerpots does she have in the house?

Algebra -> Word Problems Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures

Question 4 - What's the Number?

Find a three-digit number that, when we add 1 to it, is divisible by 7; when we add 2 to it, is divisible by 8; and when we add 3 to it, is divisible by 9.

Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules

Question 5

Consider all the numbers from 1 to 4242. Find the difference between the number of odd numbers divisible by 3
and the number of numbers divisible by 7 in this range.

Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules Arithmetic -> Fractions Number Theory -> Division

Question 6 - Hexagon

In the diagram, there is a regular hexagon. By what factor is the area of the white region larger than the area of the shaded region?

(A regular hexagon is a hexagon where all sides are equal and all angles are equal.)

Geometry -> Plane Geometry Geometry -> Area Calculation

Question 7 - Long Division

Calculate the value of the expression and write it as a decimal fraction:

`1/(1+1/(1+1/(1+1/(1+1/(1))))`

Arithmetic -> Fractions Number Theory -> Division

Question 8 - Differences in the Multiplication Table

Color the `10xx10` multiplication table with a black and white chessboard coloring, such that the cell of `1xx1` is colored black.
Find the difference between the sum of all the numbers in the black cells and the sum of all the numbers in the white cells.

	1	2	3	4	5	6	7	8	9	10
1	1	2	3	4	5	6	7	8	9	10
2	2	4	6	8	10	12	14	16	18	20
3	3	6	9	12	15	18	21	24	27	30
4	4	8	12	16	20	24	28	32	36	40
5	5	10	15	20	25	30	35	40	45	50
6	6	12	18	24	30	36	42	48	54	60
7	7	14	21	28	35	42	49	56	63	70
8	8	16	24	32	40	48	56	64	72	80
9	9	18	27	36	45	54	63	72	81	90
10	10	20	30	40	50	60	70	80	90	100

Arithmetic Combinatorics -> Number Tables Combinatorics -> Colorings -> Chessboard Coloring

Additional sources:

Young Mathematician Olympiad, 2017-2018, Stage A, Grades 3-4 Question 8

	1	2	3	4	5	6	7	8	9	10
1	1	2	3	4	5	6	7	8	9	10
2	2	4	6	8	10	12	14	16	18	20
3	3	6	9	12	15	18	21	24	27	30
4	4	8	12	16	20	24	28	32	36	40
5	5	10	15	20	25	30	35	40	45	50
6	6	12	18	24	30	36	42	48	54	60
7	7	14	21	28	35	42	49	56	63	70
8	8	16	24	32	40	48	56	64	72	80
9	9	18	27	36	45	54	63	72	81	90
10	10	20	30	40	50	60	70	80	90	100

	1	2	3	4	5	6	7	8	9	10
1	1	2	3	4	5	6	7	8	9	10
2	2	4	6	8	10	12	14	16	18	20
3	3	6	9	12	15	18	21	24	27	30
4	4	8	12	16	20	24	28	32	36	40
5	5	10	15	20	25	30	35	40	45	50
6	6	12	18	24	30	36	42	48	54	60
7	7	14	21	28	35	42	49	56	63	70
8	8	16	24	32	40	48	56	64	72	80
9	9	18	27	36	45	54	63	72	81	90
10	10	20	30	40	50	60	70	80	90	100

	1	2	3	4	5	6	7	8	9	10
1	1	2	3	4	5	6	7	8	9	10
2	2	4	6	8	10	12	14	16	18	20
3	3	6	9	12	15	18	21	24	27	30
4	4	8	12	16	20	24	28	32	36	40
5	5	10	15	20	25	30	35	40	45	50
6	6	12	18	24	30	36	42	48	54	60
7	7	14	21	28	35	42	49	56	63	70
8	8	16	24	32	40	48	56	64	72	80
9	9	18	27	36	45	54	63	72	81	90
10	10	20	30	40	50	60	70	80	90	100