**General instructions.** Short Answer: there are 20 questions, fill in the correct answers in the space provided after each question. Each correct answer is worth 2 points. Time limit: 60 minutes.
Henry was given a certain number to multiply by 507, but he placed the first figure of his product by 5 below the second figure from the right instead of below the third. The result of Henry’s mistake was that his answer was wrong by 382050. What was the multiplicand?
Mice have 4 legs, ants have 6 legs and spiders have 8 legs. Eddy has twice as many mice as spiders, and three times as many ants as spiders. The number of legs adds up to 68. How many spiders does he have?
There are 100 nuts in five bags. In the first and second bags, there are altogether 42 nuts; in the second and third bags, there are 43 nuts; in the third and fourth bags, there are 34 nuts; in the fourth and fifth bags, there are 30 nuts. How many nuts are there in the first bag?
A student had to multiply 169 by a two-digit number whose second digit is twice as big as the first digit. Accidentally he changed the places of the two digits and obtained a product that differed from the correct one by 4563. Find the two-digit number.
A collection of sheep and turkeys have a total of 99 heads and legs between them. There are twice as many turkeys as there are sheep. How many turkeys are there?
Each of the letters A, B, C, D, E is used to represent a single digit in these two statements. (Same letter = same digit.) $A+B=C$, $C+D=\overline{EA}$ (Note $\overline{EA}$ is a 2-digit number). What is the value of $B+D$?
Ann, Ben and Carol each have some money. If Ann gave Ben 30 dollars, then Ben would have twice as much as Ann. If Ben gave Carol 30 dollars, then Carol would have twice as much as Ben. If Carol gave Ann 30 dollars, then they would both have the same amount. How much money did Ann have?
A square lawn has a path 1 m wide which goes around the outside of all the four edges. The area of the path is $40\text{ m}^2$. What is the area of the lawn?
A cube with an edge length of 10 cm is resting on a horizontal table. An insect starts crawling from the table at an angle of 30 degrees to the horizontal. How far will it have crawled on the cube by the time it gets to the top?
On this diagram you may start at any square and move up or down or across (but NOT diagonally) into the next square. No square may be used twice. The digits in each square are written down in the order they are used to form a number. What is the largest number that can be made?
A new monument is to be made in the shape of a cuboid. Only three of the faces are to be decorated. To allow for this: one face has to have an area of $48\text{ m}^2$; another is to have an area of $72\text{ m}^2$; and another of $96\text{ m}^2$. What will be the volume of the monument?
Arrange the numbers 1 to 9, using each number only once and placing only one number in each cell so that the totals in both directions (vertically and horizontally) are the same. How many different sums are there?
A 4-wheeler car has travelled 24,000 km and, in that distance, has worn out 6 tyres. Each tyre travelled the same distance. How far did each separate tyre travel?
A, B and C are three villages near to each other, shown in the diagram below, where the straight lines represent the only roads joining the villages. The figures give the distances in km between villages.
A new fire station is to be built to serve all three villages. It is to be on a roadside at such a position that the greatest distance that the fire-engine has to travel along the roads in an emergency at one of the villages is as small as it can be. What is this smallest distance?
