Bebras SMP-SMA 1

A robot is programmed to collect as many sweets as possible. It does this while walking through cells. Each cell in the grid has either 0, 1, 2 or 3 sweets.

The robot begins in the bottom-left and ends in the top-right. The robot can only move to the right or upwards.

Question:

How many sweets will the robot collect in this grid?

• 10

• 12

• 14

• 16

The teachers at Funtime School like to include games in their lessons.

At the end of one day, one teacher invites his students to play a game. The winner gets to leave school before the others are dismissed.

Rules of the game:

The school has one corridor with five doors in a row. The students form a queue and take turns to walk down the corridor. When they get to an open door, they must close it and move to the next door, When they get to a closed door, they must open it, go into the calsswroom, leave the door open and wait there until the teacher dismisses them.

At the start of the game all the doors are closed.

If a student finds all the doors are open, after shutting each of them, they can head home for their tea!

Question:

If the students are numbered 1 to 35, which student gets to leave school first?

• 35

• 25

• 10

• 32

We define a basic operation as one of the following:

-insert one character into a word

-remove one character from a word

-replace one character with another.

We define the distance between two words as the minimum number of basic operations which allows us to change the first word into the second.

For example, the distance between kitten and sitting is equal to 3. The basic operations necessary are:

-kitten → sitten (change k to s)

-sitten → sittin (change i to e)

-sittin → sitting (insert g at the end).

Question:

What is the minimum distance between length and french?

(Enter integer value)

When downloading files from a server, the download speed is limited.

For example, when 10 files are downloaded simultaneously, the download speed for each file is 10 times slower than it would be for only one file.

A user simultaneously downloads three files from a server.

The picture shows the current download state.

Note that the time remaining for each file is computed based only on the current speed and does not depend on any history.

Question:

How many minutes will it take to download all the files?

(Enter integer value)

There are five drinking glasses on the table.

One of them is turned upside down.

In this game, you have to get all glasses upright again.

But: you have to turn exactly three glasses every turn.

How many turns do you need at least to get all the glasses standing upright?

• It's Impossible

• 3 times

• 5 times

• 2 times

A device in a medical lab must repeatedly shake specimens taken from patients.

The device works according to a computer program, which is written on numbered lines. The device reads the program line by line. It always reads one line and then executes it immediately. If the line contains the command go to step X, the device jumps to step X and continues reading and executing.

"A" represents the number of times the device shakes the specimens. The program is able to store a number A, to add 1 to the number stored in A, and compare its value with another number.

The Program:

Step 1: Set A to 0.

Step 2: Add 1 to A.

Step 3: Go to step 6.

Step 4: If A equals 6, go to step 8.

Step 5: Set A to 0.

Step 6: Add 1 to A.

Step 7: Go to step 2.

Step 8: Shake the specimens A times.

Step 9: End

Question:

How many times will the device shake the specimens when this program is run?

The specimens will never be shaken.

• The specimen will never be shaken.

• The specimen will be shaken once.

• The specimen will be shaken 60 times.

• The program will not stop the specimens being shaken.