BEBRAS 2025 Grade 7-8 Round 2 Ext

Captain Ben is aboard his boat but does not know its position. Each circle on his map marks where the light of that lighthouse is visible.



He sees lights B and C, but not A. Which numbered position is his?

Machine A joins input sheet 1 above input sheet 2. Machine B rotates both input sheets and joins sheet 1 to the left of sheet 2, as illustrated.



The beaver combines the machines as follows.



Which pictured sheet results?

Four jigsaws each contain sixteen pieces in a 4×4 grid. Corresponding pieces have the same size and shape but may have different colors or patterns.



The beaver takes the complete first jigsaw and enough extra pieces from the others to assemble any one of the four pictures. What is the remainder when the smallest number of extra pieces is divided by 4?

Beavers live in the pictured nests. Road segments meet at trees and all segments have equal length. Each beaver will take a shortest route from its nest to the meeting tree.



Which tree minimizes the largest distance any beaver must travel?

Nam has a transparent ring containing marked balls. Shaking moves the balls as shown in the example.



After another shake, how many of the seven pictured rings could be the result?

A beaver uses this decision chart to test whether a number is beautiful. The tests ask divisibility by 4, then by 100, then by 400. A failed first test is not beautiful; passing 4 but failing 100 is beautiful; passing 100 is beautiful only if 400 also divides it.



For example 83 is not beautiful because 4 does not divide it. How many of 1900,2000,2024,2025,2200 are beautiful?

Alice prepared fourteen gifts, each normally weighing exactly 100 g, but left her phone inside one. She keeps boxes in increasing label order, divides the selected group into two nearly equal consecutive parts, and weighs the first part. If it is heavier than its normal total, she keeps it; otherwise she keeps the second part. When the group size is odd, the first part has one fewer box. She repeats until one box remains.



In which listed box would the phone require the fewest weighings?

The beaver encodes letters with this table.



A green bead denotes a dot.



A long purple bead denotes a dash.



A small red bead separates letters.



Here is the example LOVE.



Which bead string encodes PEACE?

A chest checks an entered password from left to right, spending one second per character. It sounds an alarm immediately on the first wrong character. Thus two correct characters followed by a wrong third character cause an alarm after three seconds. The record below has unreadable characters shown by asterisks; these are missing recorded letters, not wildcard inputs.



The eight trials, in order, alarm after 1,8,7,2,4,9,5,10 seconds. Among the first nine password characters, how many different letters occur more than once?

A language machine has left and right input strings. Repeatedly take the last character of the right string and append it to the output, then take the last character of the left string and append it. Stop when at least one input is empty, and append any remaining letters from the other input. The examples show the rule.



What is the output for left COMPE and right TITION?

The maze contains thirty-five chestnuts, shown as black dots. The beaver starts at S. It moves one cell up, down, left or right and takes the chestnut in each cell it enters. It cannot cross black walls or enter a cell without a chestnut.



What is the maximum number it can collect before leaving by W,X,Y or Z?

Two boxes X and Y each have ten numbered compartments containing apples (A) or oranges (O), as shown.



Move[m,n] swaps the fruits between X and Y at every corresponding position m through n. Magic[m,n] changes each fruit in both boxes at positions m through n to the other type. Apply Magic[5,7], then Move[2,5], then Magic[7,10]. How many more apples does X then contain than Y?

Five beavers Anala, Devi, Hem, Jay and Raj took part in a competition described in the source as having six races. The supplied table lists the following races.



Table rows give month, turns, length, direction, downhill and uphill; “Thuận” means forward, “Ngược” reverse, “Có” yes and “Không” no. Raj and Jay run better on courses with at least twenty turns. Hem does not run well in reverse. Raj likes uphill courses. Anala runs best on courses longer than 3 km. Devi runs best on courses with an odd number of turns and longer than 3 km. Anala won earliest, and each runner won one race. Who won Diri?

A matching-card game requires every pair of cards to have exactly one symbol in common. The example shows three four-symbol cards with their shared symbols.



Alice and Bob now have these six numbered cards.



How many choices of one card to remove leave a valid set?

Boats are decorated with triangular, rectangular or square flags. Each boat uses one flag type. Some are already decorated as shown; the vertical arrow labels mean above and below.



Every undecorated boat receives the same flag shape as the nearest boat immediately above it along its branch. Repeat until all boats have flags. How many boats finally have triangular flags?