A truck delivers apples from a warehouse to three stores.
Its signal panel tells it where to go: star
means store 1; crescent
means store 2; triangle
means store 3. Several signals may appear together. Store 1 has highest priority; stores 2 and 3 have equal priority. After a delivery and return to the warehouse, all signals disappear. One afternoon the truck goes to store 1, then store 2, then store 1 again. Which set of three received signal boards is possible?
The columns, left to right, are Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday. Beaver makes these true observations:
- Mai wears ... on Monday and Wednesday.
- Whenever Mai wears the blue skirt
, she also wears ... .
- Mai uses ... only on Saturday and Sunday.
- Mai uses ... on Friday but not Thursday.
Which four clothing items fill the blanks in order?
Alex wants to install the fewest security cameras for ten houses connected as shown. A camera at a house protects that house and every other house connected to it by one straight segment in the picture. For example, a camera at house 1 protects houses 1,2,3,4.
What is the minimum number of cameras needed to protect every house?
A pirate island is divided into sixteen regions numbered 1–16, exactly one of which contains treasure. Captain Boris can enter any set of region numbers into a device, which answers whether the treasure is in one of those regions. For example, entering 1,5,12 and getting “yes” means it is in region 1,5 or 12. What is the smallest number of uses that guarantees Boris can always identify the treasure’s region?
Beaver organized three forest tours and learned these tree-preference orders.
“Chuyến” means “Tour”; the less-than signs point from less liked to more liked. On a new tour Beaver wants to present these five trees in increasing preference order.
Which order avoids contradicting any earlier information?
In words: apple→dragon fruit; dragon fruit→banana; starfruit→pineapple; pineapple→grapes; grapes→apple; banana→starfruit. Ben may apply the transformation repeatedly. The source says an apple can become a dragon fruit and then a banana, and prints this example formula:
Yesterday Ben applied the following five nested transformations:
Tim encodes BEBRAS, TURTLE, WEASEL, WALRUS and IGUANA by replacing equal letters with equal symbols and different letters with different symbols. He obtains these five strings.
A conveyor continuously carries toys in the arrow direction shown.
The boxes are labeled Balls, Cars and Airplanes. Beaver sorts all toys into the three boxes: after picking one toy, skip the next remaining toy, then pick the following toy, continuing until the belt is empty. Beaver wants the airplane to be the last toy put away. Which toy must be picked first?
An animal can jump over any shorter animal. When its name is called, it successively jumps over all shorter animals immediately ahead of it. What is the minimum number of animals that must be called to obtain increasing height from the back of the line to the front, which is left to right in the picture?
SuperBeaver’s scrolling background is a sequence of six tiles. The computer repeatedly appends a new tile on the right while deleting the leftmost tile.
To choose the next tile, it follows an appropriate arrow from the preceding tile in this transition diagram.
“Phông nền” means “Background”; “Sơ đồ” means “Diagram”. Which sequence cannot be a SuperBeaver background?
Nick hides food beneath some of the eleven trees around a pond. His map is shown.
A number in a square gives the number of food-containing tree cells adjacent horizontally, vertically or diagonally to that square. What is the least number of trees beneath which Nick hid food?
