## August 2015 Logic & Maths Problems

1. This pyramid has an unusual property: Every brick has a number, and for levels two, three, four and five, each brick’s number is the sum of the numbers of the two bricks that it sits on. Write down the numbers that belong to bricks a, b and c respectively.

2.
For each piece of rope as shown, state whether a knot will be formed when the two ends are pulled apart.
When one strand of rope passes over another, the lower strand is represented with a break, thus:

3. In a supermarket, the aisles are numbered 1 to 6 from the entrance.
Washing powder is in the aisle next to the aisle containing the bottles of tomato sauce, and is not in the first aisle you see when entering the supermarket.
You see the meat aisle sometime before you encounter the bread aisle.
Tins of jam are two aisles before the bottles of tomato sauce and the meat is four aisles after the fresh fruit.
If all six aisles have been mentioned:

a. What is in the first aisle (aisle 1)?
b. What is in the last aisle (aisle 6)?
c. In which aisle are the bottles of tomato sauce?

4. Given that there are officially only eight planets left in our Solar System, write the three most common letters in the combined names of those planets, in descending order of frequency.

5.
In many liquor stores you can buy pear brandy, with a real pear inside the bottle. The pear is whole and ripe, and the bottle is genuine; it hasn’t been cut in any way. How did the pear get inside the bottle?

6.
Here are two license plates with interesting configurations. All the letters on both license plates have a logical order, except for one. There is a single letter on Set 2 that belongs on Set 1. Can you find it?

7.
The measuring cylinder on the left contains a litre of milk, the other a litre of water. Take one tablespoon of milk and mix it with the water. Now take one tablespoon of the water/milk mixture and mix it in with the pure milk to obtain a milk/water mixture. Is there:
A. more water in the milk/water mixture?
or
B. more milk in the water/milk mixture?
or
C. the same amount of water in the milk in the LHS cylinder as there is milk in the water in the RHS cylinder?

8. Draw the symbol that comes next in this sequence

9.
The above diagram shows a green quarter-circle on which a brown rectangle has been superimposed. How long is the dark blue line?

10. Young Bill takes his dog Fido for a walk. He spots his best friend Fred exactly two kilometres away. Bill and Fred immediately start running toward each other at 10 km / hr each. At the same time, Fido slips his lead and runs directly toward Fred at 25 km /hr. As soon as he reaches Fred, he turns around and runs back to Bill. He then runs backward and forward between Bill and Fred until the two boys meet.
Assuming all travel is in straight lines and at constant speeds, how far will Fido have run between the time that the two boys first see each other until the time they meet?
Hint: there are a number of difficult ways of working this out. There is also an easy way.

SOLUTIONS