On the social network TeeniGram, each user can follow other users. In a group of TeeniGram users, a person is called an “Idol” if everyone else in the group follows that person and that person does not follow anyone in the group. In a group of five beavers, Alan, Don, Frances, Grace and Robin:
- Alan follows Don and Grace.
- Don follows Grace and Robin.
- Frances follows Alan, Grace and Robin.
- Robin follows Alan and Grace.
Who is the idol in this group?
A beaver is going for a morning run. The beaver plans to visit locations 1, 2, 3 and 4, not necessarily in that order, along the grid lines in the park shown below. Each grid square has side length 100 meters.
The grey muddy areas in the park cannot be crossed. What is the shortest distance, in meters, that the beaver can run to visit all four locations?
A beaver must pack 5 large balls, 2 medium balls and 5 small balls into boxes. There are 3 large boxes, 5 medium boxes and 3 small boxes. A ball fits into a box of the same size or a larger size. Each box can contain exactly one ball.
What is the maximum number of balls the beaver can pack?
There are three groups of snowmen, with five snowmen standing in a row in each group. From left to right, each snowman takes a hat from a stack, working from the top down.
How should the groups of snowmen be matched to the stacks of hats so that every snowman gets a hat of the right size?
A beaver draws pictures by scraping away the grey top layer of a sheet of colored paper, as shown below:
Which picture below reveals exactly three colors from the color layer underneath?
Rebecca the beaver has cubes of different sizes, as shown below. The numbers represent the cubes’ sizes.
Rebecca wants to arrange the cubes from smallest to largest, from left to right, by repeatedly swapping two neighboring cubes. What is the minimum number of swaps needed?
A beaver chef keeps secret recipes in a safe. The safe has the dial lock shown below.
To open the safe, the beaver turns the arrow alternately left and right so that it points to the letters of the password in order. For example, to reach B and then H, the beaver turns 1 step clockwise and then 2 steps counterclockwise, as shown below.
How should the beaver turn the dial if the password is CHEFDG?
Diana the beaver must decorate five banquet tables for an upcoming holiday. Diana can use:
- Two types of tablecloth:
- Three types of flower:
The decorated tables must satisfy these conditions:
- Either all three flower types are used, or exactly one flower type is used.
- Neighboring tables must not have the same type of tablecloth.
Which arrangement below satisfies the conditions?
The machine below adds items to the cup underneath as follows:
- Pressing button 1, 2 or 3 drops the leftmost item from the corresponding tray into the cup.
- Pressing button 4 removes the item most recently added to the cup.
For example, pressing buttons 1, 2, 4 and 3 in that order produces the cup shown in Figure 2.
Starting from Figure 1, the beaver presses 3, 1, 1, 4, 4, 2, 3 and 4 in that order. Which item is second from the top of the cup?
To get home, a beaver must travel downstream along each river, following the arrows in the diagram.
How many different routes can the beaver take home?
A black-and-white computer image is divided into a grid of small squares called pixels. Each square is either white or black. Each row is then encoded using the runs of white and black squares, in that order. For example, the letter “a” is encoded by the sequence below. Each dash marks the start of a new row.
1,3,1 – 4,1 – 1,4 – 0,1,3,1 – 0,1,3,1 – 1,4
Which image below is encoded by 2,1,2 – 0,1,3,1 – 1,1,1,1,1 – 2,1,2 – 1,1,1,1,1 – 0,1,3,1?
A room has three light bulbs, X, Y and Z, and four switches:
- Switch 1 turns Y on and X off.
- Switch 2 turns X and Y on and Z off.
- Switch 3 turns Z on and Y off.
- Switch 4 turns X on.
All the bulbs are initially off. A beaver wants all three bulbs to be on. Which sequence of switches below achieves this fastest?
If a bulb is already on (or off), pressing a switch to turn it on (or off) does not change its state.
Five beavers are sitting in a row, as shown below.
Among them are two sisters who are not sitting next to each other and two brothers who are not sitting next to each other. Of reporters X, Y and Z, one is lying and two are telling the truth.
- X says: “Every female beaver is sitting next to a male beaver.”
- Y says: “Exactly one male beaver is sitting next to a female beaver.”
- Z says: “There are exactly two male beavers.”
Which statement below is correct?
Y is lying, and the middle beaver is male.
Y is telling the truth, and the middle beaver is male.
Y is lying, and the middle beaver is female.
Y is telling the truth, and the middle beaver is female.
Two types of beaver take part in a race: grey beavers (G) and white beavers (W). There are six entrance paths and six exit gates, as shown below.
Whenever a beaver reaches an intersection, it must wait until another beaver is at that intersection too.
- If the two beavers have the same color, one goes left and the other goes right.
- If they have different colors, the grey beaver goes left and the white beaver goes right.
At the end of the race, the exit order from left to right is WGWGWG. What was the beavers’ order at the six entrances, from left to right?
The beavers have a common rule: always pay using as few coins as possible. For example, to pay 17 coins, they take one 16-value coin and one 1-value coin rather than seventeen 1-value coins. What is the smallest number of coins needed to pay 13?
Six beavers, NICOLE, KEVIN, KRISTINA, EDGAR, KATEY and NATHANAEL, play a game with their teacher. The teacher must find a beaver whose name satisfies these conditions:
- It contains G or I.
- Its last letter differs from the first letter of every other beaver’s name.
- Its first letter is also the first letter of another beaver’s name.
Paul the beaver has four stamps A, B, C and D, as shown.
He used stamp B four times to make figure 1. Paul used stamp B once and stamp D twice to make figure 2. To make figure 3, which stamp can Paul definitely not use?
