Otago Problem Solving

As an optional choice, you can sign up for Otago Problem Solving. This is an opportunity where roughly every month you have a sheet of five questions to answer in 30 minutes. The questions get progressively harder, so the fifth one might take you ten minutes or more. After five of these sheets, if you have 20 or more answers correctly answered, you can take the second part of the exam, which is a 40 question long quiz that again gets more difficult with the number of the question. It's a good time to practice all areas of mathematics.

Here's an example of the questions from a previous year. See how many of them you can answer!

1. The number of dots on opposite faces of a dice always add up to 7.
Two views of the same dice are shown here.

What's the number of dots on the top face (pointed at with the arrow?)

2. While driving the 75km from Aston to Combe, Kim noticed that Bream to Combe was 11km more than Aston to Bream.

How far is it from Aston to Bream?



3. The five-digit number 2AA6B is divisble by both 5 and 9 but not 2.

What digits are A and B?


4. At the bread shop, Mrs Green bought half of all the loaves for sale plus an extra half a loaf. The Mrs Brown bought half of all the loaves for sale plus an extra half a loaf. Then Mrs Black bought half of all the loaves for sale plus an extra half a loaf. There were no loaves left. 

How many loaves were there at the start?


5. Each letter can be replaced by a different digit to make this sum correct.

What is the answer (C A K E?)

    E A T
+  T E A
_______
 C A K E