Residents paint each house blue (B), red (R), or green (G). A house must differ in color from its immediate neighbors on the same side of the street and from the house directly opposite. Some colors are already fixed.
Bob wants to use his mother’s computer. Its password consists of her name Emily with exactly one uppercase letter, and her two-digit age placed either before or after the name. Bob knows her exact name and age. What is the smallest number of attempts that guarantees finding the password?
Anna, Ben and Lisa live in three houses colored blue, red and yellow, one of each. They have different pets: a cat, a parrot and a dog. Anna lives in the yellow house. Ben lives next to Lisa. The red house has the cat. Lisa has the parrot. Which statement must be true?
In a chess tournament an arrow goes from winner to loser. For example Emma beat Bob and Isaac beat Henry.
By transitivity, if X beat Y and Y beat Z, X is considered to have beaten Z. The champion must beat every other player under this rule. Four more games have these results.
Kangaroo wants to reach home at the bottom-right corner. It can travel horizontally or vertically along the drawn roads, and can cross a rock pile only if it contains at most two rocks. One segment joins two neighboring junctions.
What is the minimum number of segments needed to reach home?
Beavers make a bracelet by joining a star bead to a moon bead, repeating this twice more to make three pairs, joining the pieces into a chain, adding two more stars, then closing the chain into a ring.
How many of these five bracelets definitely cannot be made this way?
A kingdom has islands A–F. Experts must travel from A to F to help with an outbreak. Travel follows the arrows, and each number is the maximum people allowed on that directed route in one day.
What is the maximum number of experts who can reach F on the first day?
A beaver has two carrots and wants one pine tree and one bundle of grass. Each castle room offers the following exchanges, from the first item to the second. A: carrot→fish or coin→grass. B: fish→rice or ring→ice cream. C: ice cream→coin or ring→grass. D: carrot→rice or carrot→ice cream. E: carrot→coin or ring→pine tree. F: ring→coin or ice cream→fish. G: ice cream→ring or carrot→grass. H: carrot→grass or rice→fish. What is the minimum number of rooms to enter to obtain both required items?
Secret information is stored in logs, classified by number of rings, lengthwise lines, and knots. The original attribute illustration labels these three quantities.
Follow the decision diagram; its pictured example log goes to area D.
Alex has nine balls and a wooden box with nine cells arranged in three rows and three columns. Any number of the balls may be used, with at most one ball per cell. The number of balls in every row and every column must be odd.
How many different arrangements satisfy all these conditions?
A Bomino tile is a 3×3 grid with gray cells. Every gray cell must share an edge or corner with at least one other gray cell. Every gray cell may share an edge with at most one other gray cell. A tile with n gray cells is called n-Bomino. Tiles that become identical by rotating or reflecting the whole tile count as the same. The examples show a 2-Bomino and a 4-Bomino.
Hansel and Gretel play with three blue stones and seven red stones. On each turn a player removes either one or two blue stones, or one, two or three red stones. Whoever takes the last stone wins. Gretel moves first and both play perfectly. Which first move guarantees her victory?
A beaver plants 16 trees, four of each of four different heights, in a 4×4 garden. Each row and column contains each height exactly once.
A sign on a side states how many trees are visible along that row or column: a taller tree hides shorter trees behind it. Here is an example with a side view.
The actual clues and positions A,B,C,D are below.
Which pictured list gives the trees at A,B,C,D, in that order?
