Bruce and Beatrix make a bead string. Bruce gives coded instructions and Beatrix adds beads: OFF (TẮT) means BLACK (ĐEN), and ON (MỞ) means WHITE (TRẮNG). The original table says “Bruce says” and “Beatrix adds colored beads to a string.”
Bruce repeats “ON OFF OFF ON OFF OFF ON OFF” until the string is full. Which illustrated section cannot belong to this string?
In Frankenstein's laboratory a scientist breeds imaginary hybrid animals. The source prose says each offspring takes its head from its father and body from its mother. The top header contains fathers, and the first column contains mothers. The source gives this cat-and-dog example:
A new experiment uses cows, owls, dinosaurs and lions.
Five offspring images have been placed in the W,X,Y,Z table, but one is said to be wrong. Which illustrated animal was incorrectly placed?
Editorial convention for the conditional answer: the example's visual legend and offspring actually use the row for the head and the column for the body, reversing the prose. Use this visible table convention below; the contradictory prose is preserved above.
A beaver family packs apples for market. First, put 8 apples in each bag, leaving leftover apples loose. Next, put 8 bags in each box, leaving leftover bags outside boxes.
After packing 275 apples, which combination of boxes, loose bags and loose apples results?
Mike's car factory has three teams: engine production, body production and painting. Each team needs 90 minutes per car. Originally the body team starts after the engine team finishes, and painting begins after another 90 minutes. Thus one car takes 270 minutes, as in the chart (“Số xe”=car count; “Thời gian”=time).
A friend suggests that all three teams work at the same time on different cars. After the first car is completed, how many minutes are needed between successive new cars?
Ten beavers need computers to write and edit their school newspaper. Red cells in the timetable indicate required time slots. The rows are beavers 1–10; columns are 8:00,9:00,10:00,11:00,12:00,13:00,14:00. All computers are identical, and each can serve at most one beaver at a time. What is the minimum number of computers?
Bobi needs seven logs of length 4 m and seven logs of length 3 m to build a dam. Only 10 m logs are available in the store. What is the minimum number of 10 m logs that must be cut?
Beavers play on logs arranged as a 3×3 grid of squares with extra diagonals, as shown. The teacher calls a number, and they must travel from the start (“Bắt đầu”) to the finish (“Kết thúc”) across exactly that many logs. If the number is 5, how many different routes are possible?
Seven athletes ski on a frozen river, starting as shown. To save energy, after every minute the athlete at the front moves to the back. Who is at the front after one hour?
Seven beavers walk around seven chairs while music plays, and sit on the nearest chair when it stops. A chair may hold several beavers. Initially A is at chair 1, E at 2, D at 3, C at 4, G at 5, B at 6 and F at 7, as shown; chair numbers increase clockwise.
In each music round, adults A,B move 3 chairs counterclockwise, teenagers C,D move 2 counterclockwise, and children E,G,F move 1 clockwise. Which chairs are empty after three rounds?
Kim must go from home (“Nhà”) to the grocery shop (“Cửa hàng”) to buy vegetables, avoiding cells with rocks or trees. Moves are only left, right, up or down. A friend is visiting, so Kim must choose a shortest route. How many shortest routes are there?
Trava is lost in a 6×6 forest containing two old trees and one rock, as shown.
Distance is the minimum number of horizontal/vertical cell-to-cell moves. For example, the rock is distance 4 from the nearer tree. Trava can see an object only if its distance is at most 4. Trava's distances from the two trees are 4 and 2, and the rock is not visible. How many cells could contain Trava?
Criminals build 16 walls between Superbeaver and the city, as shown. Superbeaver can see through exactly one wall. What is the minimum number of walls to destroy so that Superbeaver can stand by the river and look into the city?
Editorial convention for the conditional answer: require visibility across the entire pictured city frontage, along the vertical sightlines drawn, with at most one retained wall on every sightline. The original wording does not explicitly say “entire frontage”; this stronger interpretation is needed for the listed choices.
A vacuum robot has three commands: F moves forward one cell and takes 1 minute; R turns right 90° and takes no time; W cleans the current cell and takes 1 minute. It cannot enter cells containing furniture. It starts and finishes at corners A,B,C or D of this 6×6 floor. What is the minimum time to clean every accessible floor cell?
Homestead Dam has four chambers A,B,C,F joined by tunnels. A,B,C are bedrooms and F stores food. Ten beavers wake up in A and want breakfast in F.
Each tunnel carries at most one beaver at a time, and crossing takes 1 minute. There are 4 tunnels A–B,1 A–C,2 B–C,1 B–F and 3 C–F. Every chamber can hold all ten beavers. What is the earliest time when all ten can be in F?
Beaver City's park is a 16×16 grid with some trash cells. Lucy has robots whose square operating areas may be 1×1,2×2,4×4 or 8×8. Each robot can clean exactly one cell within its area. The areas must cover the whole park exactly: every cell covered, no overlaps. Black cells in the diagram contain trash. What is the minimum number of robots needed to clean all trash?
