Billy Beaver writes down his favourite numbers, from smallest to largest when read from left to right.

Roberta Beaver has purchased an old computer that only allows one digit after the decimal point in any calculation. Anything after that digit is removed. Sometimes this results in an error which is the difference between the stored value and the exact value. For example, if we try to compute 7 5 on Roberta’s machine, this will be stored as 1.4 which is the exact value of 7 5. This gives an error of 0. However, if we compute 7 4, this will be stored as 1.7 since 7 4 = 1.75 and “5” will be removed from the end. This gives an error of 0.05. Extra digits are removed after every operation. For example, when Roberta computes3 2
×2 3
, she computes 3 2 to give 1.5, then 2 3 to give 0.6, and then 1.5×0.6 to give 0.9. This gives an error of 0.1.

If Roberta computes10 3
×10 3

×9, what is the error?

James made 37 litres of lemonade at home and now he wants to bring it to a celebration at school. He has several empty bottles of various sizes but he wants to use the smallest number of them to bottle exactly 37 litres of lemonade. He has one bottle of each of the following sizes:

ˆ 1 litre

ˆ 2 litre

ˆ 4 litre

ˆ 8 litre

ˆ 16 litre

ˆ 32 litre

What is the least number of bottles James needs to use?

Alice, Bob, Charles, and Dorothy share two baguettes, two rolls, two croissants, and two slices of toast.

Each person has two different types of bread. Also:

• Alice and Bob do not have any type of bread in common.

• Charles has a baguette.

• Dorothy has a roll, but Alice does not have a roll.

• Bob has a croissant.

Which types of bread does Alice have?

A museum has received statues of five famous computer scientists. However, there is only room to display one statue at a time. They must decide the order in which the statues will be displayed. They come up with the following rules:

ˆ Turing before Berners-Lee

ˆ Turing before Hopper

ˆ Hopper before Lovelace

ˆ Hopper before Gates

ˆ Lovelace before Gates

What is one order in which the statues could be displayed

Bebras Tech offers the following evening classes:

ˆ Computing (C),

ˆ Geography (G),

ˆ Language (L),

ˆ Math (M), and

ˆ Science (S).

Three beavers would like to sign up for these courses:

ˆ Xavier wants to take C, L, and M;

ˆ Yvette wants to take C, G, and S;

ˆ Zoey wants to take L, M, and S.

Bebras Tech wants to squeeze these courses into as few evenings as possible such that:

ˆ each course is offered on exactly one evening, and

ˆ beavers can take at most one course per evening.

What is the least number of evenings needed for Bebras Tech to schedule these courses?

Beavers named NICOLE, KEVIN, KRISTINA, EDGAR, and KATEY play a game with their teacher. The teacher must discover the mystery beaver among them whose name satisfies these rules:

1. The name of the beaver has the letter G or I in it.

2. The name ends with a letter that no other name starts with.

3. The name starts with a letter that at least one other name starts with.

Who is the mystery beaver?

B-taro has exactly five bills worth the following amounts of money: ฿1, ฿10, ฿100, ฿1000, and ฿10000. He lists all the possible total amounts of money he can make from greatest to least.

For example, ฿11110 ranks 2nd on B-taro’s list.

Story

For example,฿11101 ranks 3rd on B-taro’s list.

Story

Where does ฿11010 rank on B-taro’s list?

Beaver Johnny received a task from his computer science teacher. He has two cards, card A and card B. On card A is a number, and on card B is a different number. Each card can only hold one number at a time. He has to exchange the numbers on card A and card B by the following three steps:

A ← A + B;

???????

A ← A−B;

The first step, A ← A+B, means that we should add the number on card A and the number on card B and replace the number on card A with this sum. The third step, A ← A−B, means that we should subtract the number on card B from the number on card A, and replace the number on card A with this difference. However, Johnny has forgotten the second step.

Which of the following is the correct second step?