A mouse is at the entrance of a pipe system and wants the cheese at the bottom of pipe 5. It follows these rules:
1. Go downward.
2. At each junction, change direction to enter the neighboring pipe.
Which entrance should the mouse use to reach the cheese at the end of pipe 5?
This table contains information about young beavers at school.
English translation, in order name / gender / age / height / favorite color / favorite subject:
- Anna / female / 8 / 1.20 m / red / Mathematics.
- Bob / male / 7 / 1.12 m / blue / Mathematics.
- Carol / female / 9 / 1.08 m / red / History.
- Dan / male / 10 / 1.20 m / black / Geography.
- Emily / female / 7 / 1.17 m / red / Physical Education.
Which query returns no result?
Select girls older than 8 and taller than 1 m.
Select boys whose favorite color is black or red.
Select girls whose favorite subject is Mathematics or Geography and who are shorter than 1.10 m.
Select boys aged at most 19 and taller than 1.12 m.
Four guests each bring one gift to a party. Each guest gives a gift to another guest, and each guest receives exactly one gift. Nobody gives to themselves. We write Art→Bran when Art gives to Bran; if Art gives to Bran and Cáit gives to Art, we write Art→Bran, Cáit→Art.
Sandra enjoys word puzzles. An Asian newspaper has a 3×3 grid of nine letters. To solve it, she must find English words that:
- include all letters in the dark cells;
- contain at least four letters.
Sandra made several puzzles and solved one of them, obtaining: Angel, challenge, clan, clean, eagle, glance, hall, heal, lane, lean.
Which puzzle did she solve?
Editorial convention: within one word, each letter cell may be used at most once; letters may be rearranged.
Bebras City has installed an electronic noticeboard. Beaver is asked to write a program to send information to it and is excited by the interesting task. In computing, a symbol may have several meanings. We know + means addition in mathematics, as in 6 + 3 = 9, but in computing it may join pieces of text.
Doctor Beaver wants to build three medical stations. No matter where a beaver is on the map, it should need to swim through at most one canal to reach a station.
Every Sunday Benno makes “Schoggimousse” for the family. He needs five eggs of equal weight. Of the six eggs on the table, five have equal weight and one is heavier; he wants to set the heavier one aside. His balance scale does not report weights, only which side is heavier, and he may put several eggs on each pan.
Benno has little time and wants as few weighings as possible. What is the smallest number of weighings that guarantees finding the heavier egg among the six?
Oh no! The famous Blue Diamond was stolen from the museum today: a thief replaced it with a fake green diamond.
There were 2000 visitors, entering the diamond room one at a time. Inspector Bebro has their names in visiting order. He asks each interviewed visitor the same question: “When you saw the diamond, was it blue or green?” Everyone answers honestly, except the thief, who says it was green. Bebro is clever and interviews as few people as possible. Which statement can he truthfully make?
I guarantee I can find the thief by interviewing fewer than 20 people.
Interviewing only 20 people is not enough unless I am lucky, but I am sure I can find the thief with fewer than 200 interviews.
This will be difficult: I need at least 200 and at most 1999 interviews.
I cannot promise anything. If unlucky, I may have to interview every visitor.
A leafy tree in the center is surrounded by two bare trees and two palms.
A monkey takes:
- 3 seconds to swing between the central leafy tree and any other tree;
- 2 seconds between a bare tree and a palm;
- 7 seconds between the two bare trees or between the two palms.
Each tree bears a different label P, Q, R, S or T. The monkey visits P, Q, S, R, T, R, P in that order. Which labels could be on the central tree if the total time is as small as possible?
Bibor and a friend play Nim. Seven matches lie in a row. The first player removes one or two matches, then the second removes one or two, and they alternate. Whoever removes the last match wins. Bibor plays first.
Hint: Bibor cannot take the last match if three remain on his turn, so he must avoid that situation.
How many matches should Bibor remove on his first turn to win?
Replacement rules describe how to rewrite a letter as a string of letters. For example, A→BB and B→ABA replace each A by BB and each B by ABA. Starting with A, these rules give A→BB→ABAABA→BBABABBBBABABB in three steps. At every step, all letters are replaced according to the rules.
Which rule set can produce BAACCACCABAB?
Editorial interpretation: the new target question does not fix an initial letter; it asks whether these rules can produce the target.
Firefighter Frank is recruiting volunteer firefighters in Beaverville. The map shows potential volunteers’ houses and the roads connecting them. He wants every house either to have a volunteer or to be exactly one road away from a volunteer’s house.
What is the minimum number of volunteers he needs?
A robot bee has four arrow buttons on its back. It moves on a square-tiled floor. The buttons mean:
Move forward one tile.
Turn left 90° without moving.
Turn right 90° without moving.
Move backward one tile.
Another button marked GO executes the stored program. For example, the following sequence moves the bee to the position shown.
The bee remembers its program, so pressing GO again executes it again from its new position and direction. You may repeat as often as desired. Repeated GO presses eventually return the bee to its starting place for all but one program below. Which is the exception?
