Alice, Bob, Emily and Tom visit an amusement park. The chart classifies four attractions by height and movement.
The vertical axis runs from ordinary height (bottom) to adventurous height (top); the horizontal axis from little movement (left) to much movement (right). Thus the Ferris wheel is high/low-motion, roller coaster high/high-motion, haunted castle ordinary/low-motion, carousel ordinary/high-motion. The source illustrates the roller coaster and carousel as examples.
Alice says she fears adventurous heights. Bob likes adventurous height and much movement. Emily enjoys movement but most wants adventurous height. Tom gets dizzy and cannot use high-motion rides. If each person takes a different ride, which list should they choose, in the order Alice,Bob,Emily,Tom?
An ordinary sandwich cookie has two biscuit layers with one cream layer between them. A beaver separates ordinary cookies to make the special sandwich shown.
The left label means ordinary sandwich cookie; the right label means the beaver’s special cookie. What is the maximum number of special cookies that can be made from 2025 ordinary cookies?
A Berukone board is a square grid of circles, some numbered. Join equal numbers by paths along grid links through unnumbered circles. Each numbered circle must have exactly one selected incident link, and each unnumbered circle at most two. The source gives one solvable and one impossible 3 × 3 example.
How many of the following four boards, numbered 1–4 from left to right, are impossible?
Lena and Paul sit together at their wedding meal. Six friends will occupy seats 1–6. Two people are neighbors if their seats are adjacent along a side or across a table corner.
- Xavier wants to see Lena and Paul in front of him.
- Rina loves music and wants to be nearest the DJ.
- Ana does not want to sit next to Rina.
- Timmy wants to sit directly opposite Karim.
- Timmy wants to sit next to Paul.
- John wants to see the DJ in front of him.
Teacher Castor makes word chains: consecutive words differ in exactly one letter. For example MUG→MUD→MAD→FAD is a chain. He partitions BOT,SAD,BAT,CAB,COT,BAD,COB,CAT,SAT into three chains of three words, using every word exactly once. Which proposed chain cannot be one of those three?
A beaver swims from the starting position to its home at D. It visits each junction A,B,C at most once. Along a river segment it may collect every log on that segment; for example the initial segment to A contains four logs.
What is the greatest number of logs it can collect by the time it reaches home?
In the library, the waiting beaver with the fewest books is served next, regardless of arrival time. The librarian takes one minute per book and finishes all books of the current beaver before calling another. Today’s arrivals and quantities are shown.
Rows: Ana 9:00,4 books; Beti 9:02,6; Cene 9:03,2; Darja 9:05,4; Emil 9:11,1. Ana arrives when the library opens and starts immediately. In what order are the beavers served?
David cycles to the park (Công viên) along the pictured route. Circular endpoints divide it into dotted or striped road segments. At each battery icon he may replace the battery, resetting its charge to exactly 20%.
The mode table is preserved below (chậm=slow, nhanh=fast, giây=seconds). For a dotted segment, slow takes 20 s and 5% charge, fast 10 s and 10%. For a striped segment, slow takes 40 s and 10%, fast 20 s and 20%. A mode can change only between segments.
Starting with 20% charge, David must not run out of charge while moving. What is the shortest travel time?
Editorial endpoint convention: a battery may reach 0% exactly on arrival at a replacement station, where it is replaced before further travel; replacement time is not specified and is treated as zero.
Leo scrambles square-grid pictures with two steps. In H, row 1 does not move, row 2 shifts right 1 cell, row 3 right 2, and row n right n−1; cells crossing the right edge wrap to the left in order. In V, columns similarly shift downward: column 1 by 0, column 2 by 1, and so on, wrapping from bottom to top. The source 3 × 3 example applies H then V.
What is obtained by applying V then H to this 1000 × 1000 image, whose top-right and bottom-left quarters are gray?
Alice and Bob alternate writing A and B in empty circles of a graph. Each has already made two moves as shown. The first player to put their own name on two directly connected circles loses. Alice moves next.
Which numbered circle should Alice choose to guarantee victory?
Alice and Bob’s secret box takes two passwords of equal length, written only with @ and #, and creates a common binary password. At each position it writes 0 if their symbols agree, and 1 if they differ.
If the common password is 0110, which pair could Alice and Bob have entered?
Two fruit boxes X and Y each have ten numbered slots containing apples or oranges. In the original legend, Táo/A means apple and Cam/O means orange.
Move[m,n] swaps the fruits between X and Y in corresponding slots m through n, inclusive. Magic[m,n] changes each fruit in slots m through n of both boxes into the other type. Apply magic[5,7], then move[2,5], then magic[7,10]. How many more apples are then in X than in Y?
There are five card types A,B,C,D,E, corresponding to the values 1,2,4,8,16. All cards of one type are identical. Each beaver takes the smallest possible number of cards whose values sum to their age.
- Fred,17, takes two cards, including C.
- Grace,18, takes two cards, including B. Her other card also occurs among Harry’s cards and is not E.
- Harry,15, is the only one with A; A is the largest value among Harry’s cards. He also takes C.
Let a,b,c,d,e be the values of A,B,C,D,E. What remainder does a−b+c−d+e+100 leave when divided by 7?
