2016 Beaver Computing Challenge
(Grade 7 & 8)
Questions
2016 Beaver Computing Challenge
(Grade 7 & 8)
Questions
Boxes are shown below. Each box is labeled with its mass in kilograms.
Xena the delivery beaver fills out a form to order boxes. For example, to order boxes totalling exactly 9 kilograms, she fills out the form as follows:
| ✓ | ✓ | |||
| 16 | 8 | 4 | 2 | 1 |
How should she fill out the form to order boxes totaling exactly 20 kilograms?
| ✓ | ✓ | ✓ | ||
| 16 | 8 | 4 | 2 | 1 |
| ✓ | ✓ | |||
| 16 | 8 | 4 | 2 | 1 |
| ✓ | ✓ | |||
| 16 | 8 | 4 | 2 | 1 |
| ✓ | ✓ | ✓ | ✓ | |
| 16 | 8 | 4 | 2 | 1 |
Beavers are preparing for a Food Festival. They would like to bake a cake but their baker is on vacation.
Keith decides to try to bake the cake. He remembers that it is important to add five essential ingredients in the correct order.
When he gets to the garden shown below, he finds a white piece of paper beside all but one ingredient. The paper shows which ingredient must be added next.
So, for example, a yellow five-petal flower must be added immediately after a pine cone. And, since there is no paper beside the strawberry, it must be added last.
Which ingredient must be added first?
An artist painted several images of a shaman. In her favourite image, the shaman
Which image is her favourite painting?
Beaver neighbourhoods consist of rivers flowing between ponds. Patricia is grumpy and wants to build one dam in each neighbourhood that will cause trouble. That is, she wants to block a single river so that beavers will not be able to travel between all pairs of ponds in the neighbourhood.
In which of the following neighbourhoods is Patricia unable to build her dam?
You have a long roll of coloured paper for a party you are hosting. The paper consists of the following pattern repeated more than once:
A beaver cut out a section of the paper between pieces of length 11 and 6 as shown below.
(...paper cut out by beaver...)
Which of the following can be the length of the paper cut out by the beaver?
The mayor of Beaverville is looking for volunteer firefighters. A map showing the possible volunteers’ homes and how they are connected by roads is shown below. He wants to ensure that every home in the town is either the home of a volunteer or is connected by a single road to the home of a volunteer.
What is the minimum number of volunteers the mayor needs?
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 \(\frac{7}{5}\) on Roberta’s machine, this will be stored as \(1.4\) which is the exact value of \(\frac{7}{5}\). This gives an error of 0. However, if we compute \(\frac{7}{4}\), this will be stored as \(1.7\) since \(\frac{7}{4}=1.75\) 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 computes \(\left({\frac{3}{2}}\right)\times\left(\frac{2}{3}\right)\), she computes \(\frac{3}{2}\) to give \(1.5\), then \(\frac{2}{3}\) to give \(0.6\), and then \(1.5 \times 0.6\) to give \(0.9\). This gives an error of \(0.1\).
If Roberta computes \(\left(\left(\frac{10}{3}\right)\times\left(\frac{10}{3}\right)\right)\times 9\), what is the error?
During his descent from the mountain top, the beaver, Theseas, is collecting wood for his lodge from several stations. Every station holds a different amount of wood. While he is descending, he cannot change direction and start climbing again, that is, he can only go in the directions of the arrows.
The paths between stations are given in the image below. Every circle is a station and the number in the circle represents the amount of wood available at that station.
What is the maximum total amount of wood that Theseas can collect during his descent?
Five beavers happily live around a circular canal. They decided to have regular meetings at one of their residences. They want to minimize the total swimming distances for them to get to the meeting place.
At whose residence will the meeting take place?
The BeaverBall is a toy operated by remote control which can be used to move the toy in four possible directions:
The BeaverBall operates inside a tower with its initial position shown below.
If the BeaverBall moves to a white square, it drops down one level falling directly onto the square below. The BeaverBall ignores commands that cause it to move outside the tower.
Which of the following lists of directions will cause the BeaverBall to reach the GOAL?
Alice the beaver plays a game with shaped cards. She starts with a single card that is a square and uses the following set of replacement rules.
meaning each square card is replaced by two triangle cards, and
meaning each triangle card is replaced by one square card, one triangle and another square (in that order).The result of following these rules three times is shown below.
Boris the beaver plays a similar game. He starts with one of a square, triangle or circle and he plays with a different set of replacement rules. The result of following these rules three times is shown below.
Which of the following set of replacement rules might Boris have used?
