ID 403

The reservoir is 70 cm wide, 70 cm long and 50 cm high. The wall thickness is 10 cm.

Which is the smallest volume?

The reservoir lays on a concrete foundation and you do not need to take into account the bottom.

ID 405

ID 407

ID 408

A symmetrical figure can be folded in half and have both sides match exactly.

Of the 26 capital letters, how many are symmetrical along the vertical axis?

ID 409

A wooden cube measures 10 cm on an edge.

What is the greatest number of small cubes that can be obtained by cutting the big cube?

ID 411

ID 413

In the figure, each number represents the length of the nearest segment.

All corner angles are right angles.

What is the area of the figure?

ID 414

ID 415

ID 418

ID 419

There are two points A and B on the grid.

We want to plot two more points and then connect all four points to form a square.

Which two points should we plot to form a square?

ID 421

ID 422

ID 423

An underground pipe drains water from a house.

The pipe must drop 11 centimeters for each 1 meter of the pipe's length.

Find the total drop d of an 11-meter-long section of this pipe.

ID 428

ID 430

ID 433

ID 436

Anna and Bob are playing tic-tac-toe on their game board. The picture shows the last position.

Which picture shows how the game board would look after being rotated (turned) 90° counterclockwise (the opposite direction of clockwise)?

ID 444

ID 445

ID 448

The perimeter of the star is equal to the perimeter of the regular hexagon.

Each side of the hexagon is 15 cm long.

How long is each side of the star?

ID 451

A rectangular greeting card has an area of 330 cm^{2}.

One side of the rectangle is 7 cm longer than the other side.

How long is the shorter side?

ID 453

Green Tennis Club members are making a logo.

The logo of the club is blue squares with a green shape.

How many blue squares are covered (partially or completely) by the green shape?

ID 455

ID 456

ID 457

Two triangles form a parallelogram with an area of 100 square meters.

What is the area, in square meters, of the left triangle?

ID 458

ID 461

We will increase the height of the photograph to 22.5 cm while maintaining the ratio of height to width.

What will be the width of the enlarged photograph?

ID 462

Anna wraps ribbon around a present. She also needs 34 more centimeters (cm) of ribbon to tie a bow.

How much ribbon does she need to wrap the present and to tie the bow?

ID 466

ID 467

The street blocks on State Street have the same length.

What is the distance between the midpoint of AB and the midpoint of CD?

ID 469

ID 471

ID 473

A 7x7x7 cube is painted, and then cut into 1x1x1 cubes.

How many of these cubes are painted on 3 sides?

ID 475

ID 480

What is the maximum number of boxes measuring 0.3m x 0.2m x 1m that can be packed into a container measuring 1.01m x 2m x 3m?

ID 483

ID 486

ID 1027

ID 1067

The tower shown is made of cubes stacked on top of each other.

Some of the cubes are not visible.

How many cubes in all are used to form the tower?

ID 1106

In a 3 x 3 grid, there are 8 lines that contain at least 3 points.

How many such lines are there in 3 x 5 grid?

ID 1108

ID 1141

ID 1214

ID 1217

ID 1338

ID 1343

ID 1381

ID 1459

ID 1473

ID 1477

ID 1496

John ate a share of a pizza and gave the other part to his friends Jim and Jack.

The diagram shows what Jim and Jack equally shared from the pizza.

How much of the pizza does Jack eat?

ID 1542

ID 1571

I cut a triangle from a square piece of cardboard as shown in the picture.

Which shape can I not form by fitting the pieces together?

ID 1606

ID 1618

ID 1627

ID 1634

ID 1654

ID 1657

The game Battleship (Battleships or Sea Battle) is a guessing game played by two people.

How many four-space battleships can you place on the 10 x 10 grid ?

They should be placed in straight lines, either horizontally or vertically, but must not overlap.

ID 1686

Find a pair of beads that are exactly the same distance apart as the length of the line segment AB.

The distance between the beads is the distance between the beads' centers.

ID 1721

ID 1725

ID 1729

ID 1762

ID 1768

ID 1772

ID 1821

What two pieces will fit together perfectly to form the same shape as the shadow shown on the right?

You may rotate the shapes.

ID 1823

I am using red and yellow tiles to make the pattern shown on the right.

If I continue the pattern in the same way, how many tiles will be in the next "circle"?

ID 1895

I drew a straight chalk line across the 8x8 chessboard.

What is the largest number of squares that the line can go through?

ID 1991

I draw a line through each pair of the vertexes of a square.

Into how many regions do I divide the plane?

Find the maximum possible number.

ID 1998

How many lines can you draw through these six points?

Each line has to pass through at least two points.

ID 2055

ISO (World Standard) drawing sizes are

841 x 1189 millimeters for A0 paper and

210 x 297 millimeters for A4 paper.

How many A4 sheets can you cut from an A0 sheet?

ID 2064

If I fold a square paper vertically, the new rectangle has an area of 32 square units.

What is the perimeter of the original square?

ID 2072

How many upper case letters look the same when rotated 180 degrees?

Remember, a rotation of 180 degrees is the same thing as rotating something until it is upside down.

ID 2778

Russia has an area of 17,075,200 square kilometers.

Canada has an area of 9,976,140 square kilometers.

The United States of America has an area of 9,629,091 square kilometers.

China has an area of 9,596,960 square kilometers.

India has an area of 3,287,590 square kilometers.

Which area is the smallest among the options below?

ID 2790

The letter 'A' is symmetrical.

A symmetrical figure can be folded in half and have both halves match exactly.

Of the 26 capital letters of the alphabet, how many are not symmetrical?

ID 2812

ID 2820

ID 2840

I assemble rectangles from colored squares.

All the squares on the edges are red, and the inner squares are blue.

For example, the figure shows a 5 x 9 rectangle with 24 red and 21 blue squares.

Find the rectangle where the number of red squares is equal to the number of blue squares.

ID 2867

ID 2878

ID 2882

Anna and Bob are playing tic-tac-toe on their game board. The picture shows the last position.

Which picture shows how the game board would look after being rotated (turned) 180° clockwise?

ID 2895

The perimeter of the star is equal to the perimeter of the regular hexagon.

Each side of the hexagon is 12 cm long.

How long is each side of the star?

ID 2913

ID 2930

Tim expands his rectangular-shaped garage. The garage is 5 meters wide and 7 meters long. He wants to triple the width and to double the length.

How does this affect the area of the garage?

ID 2960

ID 2965

ID 3288

In the picture, figures ABCDEF and UVWXYZ have the same shape and size.

Which side must have the same length as side CD?

ID 3296

ID 3320

ID 3346

Children launched 20 balloons.

They found 20 balloons.

The diagram shows where the balloons were found.

How many balloons traveled more than 15 km?

ID 3347

Children launched 20 balloons.

The diagram shows where the balloons were found.

From which direction did the wind blow?

ID 3352

A pentagon (from pente, which is Greek for the number 5) is any five-sided polygon.

How many pentagons are there?

ID 3353

A hexagon (from hex, which is Greek for the number 6) is any six-sided polygon.

How many hexagons are there?

ID 3408

ID 3603

ID 3671

ID 3720

ID 3761

Squares 1, 2, and 3 have sides of length 1, 2, and 3 units, respectively.

What is the perimeter of the entire figure?

ID 3805

ID 3902

ID 4668

ID 4792

ID 4860

ID 4868

ID 4884

ID 5055

ID 5076

How many small squares are needed to completely cover the surface of the green triangle?

You can cut the squares.

ID 5197

Can we use each of the four small shapes on the left exactly once to make the triangle on the right without any cutting or overlapping?

ID 5486

ID 5504

A shop owner installs a security camera on the ceiling of his shop. The camera can turn up-down and right round through 360°. The picture shows the design of the shop.

Where can a thief be hidden without being detected by the camera?

ID 5721

I would like to add more blocks to form a cube.

I don't move the original blocks in the pyramid.

How many blocks must be added to form a cube?

ID 5767

The sculpture is built with identical cubes.

If the sculpture weighs a total of 1540 tons, how much does one cube weigh?

ID 5890

ID 5894

The tower is made up of three horizontal layers of cubes with no gaps.

How many more small blue cubes must be added to form a large 3x3x3 cube?

ID 5976

ID 6032

ID 6081

ID 6199

Tree frogs can jump 7 feet, which is 50 times the length of their body.

Jonny the Frog is lazy today. He makes successive jumps of length exactly 2 feet.

What is the smallest possible number of jumps he can make to end exactly 7 feet eastward from the start point?

ID 6335

ID 6340

Leslie Green asks:

Although it doesn't look like it, the distances along any of the blue strings are equal because it is a 3-dimensional object.

What is the shortest distance between blobs 03 and 09?

You can only travel along a blue string.

ID 6377

I would like to open a ring so that all rings are separated.

Which ring do I need to open?

The links look like Borromean rings that are used in the coat of arms of the aristocratic Borromeo family in Northern Italy.

ID 6434

ID 6436

ID 6438

ID 6627

ID 6760

ID 6900

I can choose 36 different 3x3 squares on the 8x8 grid.

How many of them don't contain green cell(s)?

ID 7056

ID 7108

An ant goes from point A to point B along the indicated path.

Does the insect turn left or right more frequently?

ID 7159