Question bank BEBRAS 2023

Việt and Nam write numbers in the squares as shown.



At how many positions have they written the same number?

Beaver Lisa wants to make the seven-layer birthday cake shown.



She must stack the available groups of layers. She may not separate layers already stacked together. Which groups below does Lisa need?

A burger uses these ingredients: buns, meat, sauce, sausage, vegetables, onion and cheese. In the original legend, Vỏ bánh = buns; Thịt = meat; Nước sốt = sauce; Xúc xích = sausage; Rau = vegetables; Hành = onion; Phô mai = cheese.



The beaver must arrange them by these rules:
1. The sauce is above the meat.
2. The meat and cheese are below the vegetables.
3. The onion is not next to a bun.
4. Every filling is between the buns.
Which burger below satisfies these requirements?

Editorial response instruction: Select all valid options.

The shop has the apple boxes shown. Each box is labelled with the number of apples it contains.



The beaver can carry at most 10 apples to the refrigerator on each trip. What is the smallest number of trips needed to store all the apples?

A beaver community lives on six islands A, B, C, D, E and F. They want to build bridges so that they can travel from any island to any other island.



What is the smallest number of bridges they must build?

Beaver Lala threads beads onto a cord to make the necklace shown.



She wants to add a star in the middle to obtain this necklace.



What is the smallest number of beads Lala must remove to insert the star in the correct place?

The robot wants to reach the present without hitting any trees. It follows these instructions: N = up, S = down, E = right, W = left. Each instruction moves it one square.



Which instruction sequence below takes the robot to the present?

The robot bee can follow three kinds of commands, one at a time. In the icon column below, from top to bottom: move forward one square in its current direction; turn right without moving; turn left without moving.



Examples:


Now the robot bee is at the position shown, facing up.


Which command sequence will take it to the hive?

Sam uses the three kinds of hexagonal tiles below to build towers. Whenever three tiles are arranged as in the template on the right, they must be all identical or all different.



He has placed the bottom row of this tower.



What does the top tile look like?

In the picture, one circle contains numbers greater than 3. The other circle contains numbers less than 10.



One number is in the wrong place. Which number is it?

Each car has a number plate. A car may enter the car park if its plate is made only from the characters in this table.



These cars are approaching.



How many cars may enter the car park?

The beaver has the four paper strips shown.



The source says that the beaver used two identical strips to make this spiral.



Which two strips did the beaver use?

Mai and Mi have necklaces made from beads as shown.
Mai:

Mi:


They take some beads from their necklaces to make one for Việt. Their remaining beads are shown below (Mai above, Mi below).



Which necklace below did they make for Việt?

The beaver has a special rule for adding pictures, illustrated by this example.



What is the result of the following picture addition?

In Beaver Bay, six lighthouses flash according to their own codes, shown below.



For example, lighthouse A has code 0100011010. In its first 10 seconds, its states are, in order: off, on, off, off, off, on, on, off, on, off. The same pattern repeats every 10 seconds. All six lighthouses start at the same time. At which of the following times are all their lights on?

Beaver has three unusual dotted leaves as shown.



First, Beaver places leaf 2 on leaf 1 as shown and sprays both leaves with white paint.



Then Beaver places leaf 3 on top of those two leaves and sprays with gray paint.



Which leaf below could be leaf 1 after painting?

To visit Grandma, Beaver must cross the forest shown.



Which directions below lead Beaver to Grandma’s house?

Bob designs a robot beaver that follows these commands.



English translation: Tx = go to location x; G = pick up wood; D = put down wood. For example, T4T2GT4D sends the robot to the bridge, then location 2, to pick up wood, back to the bridge, and to put down the wood. The robot works in this forest:



Which program collects the wood at locations 1, 2 and 3 and puts it at location 5? To cross the river, the robot must use the bridge.

Nam, Việt, Mai and Mi each wear a hat, shirt and shoes in blue, red, purple or yellow. No two children have the same hat color, shirt color or shoe color.



The table columns are Name / Hat / Shirt / Shoes. Nam: blue / yellow / red. Việt: yellow / blue / purple. Mai: red / purple / yellow. Mi: unknown in all three columns. What colors are Mi’s hat, shirt and shoes?

Beaver brings a jar containing five candies to class. Each time, Beaver eats the candy at the top. The candies are eaten in this order:



Which jar did Beaver bring?