Nick has hidden food beneath some of the 17 trees around the pond. Each number gives the number of food-containing trees in neighbouring squares, including horizontal, vertical and diagonal neighbours.
A Berukone board is a square grid of circles, some containing numbers. Connect equal-numbered circles by paths through unnumbered circles, following the grid links. Each numbered circle must have exactly one selected incident link and each unnumbered circle at most two. Here are a solvable board and an impossible board.
How many of the following four boards cannot be solved?
Board 1:
A box is locked by an ordering of these five symbols.
The rules are:
1. The triangle is not adjacent to the heart.
2. The circle is neither first nor last.
3. The star is somewhere to the left of the triangle.
4. The heart is not adjacent to the circle.
5. The star is immediately to the right of the moon.
What position, counting from the left, does the moon occupy in the unlocking sequence?
Seven beavers join a club. A check in the table means the row and column persons already know each other.
At the first meeting the teacher gives each beaver a different message. Each shares it with everyone they know. Whenever a beaver receives a new message, they immediately share it with everyone they know. Which listed beaver receives the fewest distinct messages?
A counterfeit-money detector is given a testing frame. It places the frame on three overlapping parts of a banknote, moving top to bottom. If any tested part fails to match the frame, the note is counterfeit. The example shows tests for 1-unit notes: “Tiền thật” means genuine and “Tiền giả” counterfeit.
Six coin stacks contain 1,6,4,2,5,3 coins from left to right.
A press of A,B,C,D or E compares the adjacent stacks on its two sides. If the left stack is smaller, swap them; if the right stack is smaller, leave them unchanged. What is the fewest button presses needed to put the stacks in decreasing order?
After an emergency, beavers travel from the house to either the museum or the forest. Each circle is a transit point. Arrows show travel directions, and edge numbers count how many beavers used each segment; some counts were not recorded.
Three beavers reached the museum. What remainder does the number reaching the forest leave when divided by 4?
A turtle robot draws a circle of diameter 7 cm when given circle(7); other values produce other diameters as shown.
First the beaver enters circle(1). Whenever the robot finishes a circle, the next command increases the diameter by 1 cm. Which picture results after 30 commands?
Cards form strings of A,B,C. You may cover letters using the supplied spare cards to maximize the score. Each consecutive group of two identical letters scores 2, three scores 3, and similarly for longer groups. Each letter is counted in at most one group; isolated letters score 0. The example BCACB initially scores 0 and has spare cards A,B.
Cover the first C by A and the second C by B to obtain BAABB, scoring 2+2=4.
Leo encodes square-grid pictures using two operations. H shifts row 1 by 0 cells, row 2 right by 1, row 3 right by 2, and generally row n right by n−1, wrapping cells crossing the right edge back to the left in order. V does the analogous downward shifts in columns: column n by n−1, with wraparound. The example applies H then V to a 3×3 picture.
What results when the following 1000×1000 picture is encoded in the order V then H?
There are five types of cards. Each type always has the same letter A,B,C,D or E on the front and the same number 1,2,4,8 or 16 on the back. Each beaver takes the fewest cards whose numbers sum to their age.
- Fred, aged 17, takes two cards, one of which is C.
- Grace, aged 18, takes two cards, one B. The other matches one of Harry's cards and is not E.
- Harry, aged 15, is the only one with A; A has the largest number among his cards. He also has C.
Let a,b,c,d,e be the numbers on A,B,C,D,E. What remainder does a−b+c−d+e+100 leave when divided by 7?
Alice and Bob alternately write their initials, A and B, in empty circles of the graph. Each has already played twice, as shown. A player loses as soon as two circles bearing their own initial are connected by an edge.
Alice moves next. Which numbered circle should she choose to guarantee victory?
Colour the eight regions in the diagram using four named colours: red, yellow, green and orange. Regions sharing a boundary segment must have different colours.
Harry explores islands connected by logs, starting at the island marked “Bắt đầu” (Start). At every arrival he follows this procedure:
- If the island already has a sign, leave it unchanged. Otherwise place an arrow pointing to the island just left.
- If an adjacent island has no sign, go there.
- Otherwise inspect the current island's sign. If it is an arrow, follow it. If it is not an arrow, all islands have been explored.
The original printed procedure is retained here.
After all islands have been visited, the arrows are as shown.
