## August 2013 Logic & Maths Puzzles

1. If four apples plus three bananas plus two oranges cost \$1.60

Three apples plus two bananas plus two oranges cost \$1.26

One apple plus three bananas plus three oranges cost \$1.26

What is the total cost of one banana plus one orange plus one apple?

2. After a local Post Office burglary, five suspects were being interviewed. Below is a summary of their statements. Police know that each of them told the truth in one of the statements and lied in the other. From this information can you tell who committed the crime?

Brian said:

It wasn’t Charles

It was Alan

Derek said:

It was Charles

It wasn’t Alan

Charles said:

It was Brian

It wasn’t Eric

Alan said:

It was Eric

It wasn’t Brian

Eric said:

It was Derek

It was Alan

3.  I have a certain number of pencils and a certain number of jars.

If I put seven pencils in each jar there will be four pencils left over.

If I put twelve pencils in each jar, there will be three jars left over.

How many pencils, how many jars?

4. This is an example of a ROSETTA. It is a pattern of seven hexagons each containing a different number from 1 to 7. The centre hexagon is shaded grey.

The puzzle below is a pattern of seven overlapping rosettas.

As previously stated, each of the seven hexagons in any rosetta contains a different number from 1 to 7.

Each of the seven grey hexagons in the puzzle contains a different number from 1 to 7

Each number from 1 to 7 may only be used once in each horizontal row.

Fill in the puzzle, then for one point each, write the numbers that go in place of a, b, c, d, e and f in the form a = , b=   etc.

5. A paddock is rectangular in shape, is twice as long as it is wide and has an area of 1000 square metres.

To the nearest metre, how long is its perimeter fence?

6. Here are the numbers from 1 to 20 in words:

One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty.

Put them in ALPHABETICAL order. Which number stays where it is?

7. Hilda was playing with her building bricks when she made a tower like the one below:

How many bricks did Hilda use altogether?

8. Work out what the logical link is between these apparently unrelated words;

CHINK, TRANCE, STAIN, TUBA and PERK

Now choose three words from the following list which also belong to this same logical family of words.

CHILD, EMBARGO, LAPS, BANANA, NIGHTMARE, CONSEQUENCE, TIGER, BRAIN

9. Here are some bits of information about the four competitors in a race.

Use the clues and the grid provided to answer four questions.

a. The runner who finished with a time of 2 min 59 sec likes romance films.

b. The person who lives in WA doesn’t like sci-fi.

c. Max finished with a time of either 2 min 59 sec or 3 min 14 sec.

d. The sci-fi film buff is Joe.

e. Anthony finished before the animation film buff.

f. Max beat the ACT resident

g. Of Max and the mystery film buff, one lives in Queensland; the other lives in the ACT.

h. The runner who finished with a time of 3 min 14 sec is not Bill.

10. A marksman averaged 22 points for his first 10 rounds. After another 20 rounds his average had increased to 34 points. For two points, what was his average for the last 20 rounds?

SOLUTIONS