Bebras 2017 Posttest

The Beta Otter sends messages to its friends using 7 lights, each light can be red or blue. Beta uses the first 5 lights to indicate the letters being sent. To show that the message is correct, Beta uses the remaining 2 lights as follows: ▪ The 6th light is blue if the number of blue lights among the first five lights is even; if not then the 6th light is red. ▪ The 7th light is red if the number of red lights among the first six lights is even; if not then the 7th light is blue. Remember, 0 is an even number. For example, if Beta has determined the first five lights as: So the 6th light must be blue (because there are 2 blue lights among the first 5 lights), and the 7th light must be blue (because there are 3 red lights among the first 6 lights). So, he should use the following pattern:

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A robot works in a city. The robot walks down the street from one place to another following the directions it is given. At each intersection of several segments there is a turn (detour) and the robot will turn counterclockwise and take deviations in a certain order according to the instructions given. The instructions given are in the form of deviation sequence numbers. For example, the instructions "4 1 2" will be followed by the robot as follows:  On the first lap, take the 4th deviation.  On the second lap, take the 1st deviation.  At the third intersection, take the 2nd intersection. If the robot is initially at A, then it will follow the instructions as shown below by following the path marked in dark color as follows: Challenge: If the robot is initially at A, and follows the instructions "3 1 3 2 3", where will it end up?

• A

• B

• C

• D

Jack the Beaver rolls a die along the road without moving. To move the dice from one square to the next, Jack rolls the dice along the edge that is on the border between the two squares. He does this 7 times until the dice reaches the square containing the white dots on the right. Note that the number of dots on the opposite side of a die is always 7 (1 is opposite to 6; 2 is opposite to 5; 3 is opposite to 4). Initially, the side with 1 point (as opposed to side 6) is at the bottom of the die, as shown in the figure. After rolling the die once to the second square, the side with 2 dots (as opposed to 5) will be at the bottom of the die. Challenge: How many dotted sides of the die are at the bottom of the die when the die reaches the green square at the end?

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• 5

• 2

• 6

There are 12 places to park cars in the parking area. Each place is numbered. The image below shows the condition of the parking area on Monday and on Tuesday. Cars that are parked (on Monday or Tuesday) will definitely park in the place shown. Challenge: How many parking spaces are never filled with cars on Mondays or Tuesdays?

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• 5

• 4

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The Candy Robot is programmed to collect as much candy as possible spread out on a floor consisting of squares. This task is carried out when the robot walks through the floor plot by plot. Each tile on the floor as depicted below has 0, 1, 2 or 3 candies. Candy Robot starts from square S (for start) at the bottom left and ends at square F (for finish) at the top right. However, Robot Candy has a limitation: every time it moves, it can only move from one tile to the next tile to its right or above it. Challenge Considering Robot Candy will collect as many candies as possible, how many candies does Robot Candy collect?

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• 12

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