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Write down a number pattern for a human pyramid with 10 students on the bottom row. How many people are needed to make this pyramid?

9 The table below represents a seating plan with specific seat number for a section of a grandstand at a soccer ground. It continues upwards for another 20 rows.

Row 4 2526272829303132

Row 3 1718192021222324

Row 2 910111213141516

Row 1 12345678 a What is the number of the seat directly above seat number 31? b What is the number of the seat on the left-hand edge of row 8? c What is the third seat from the right in row 14? d How many seats are in the grandstand?

10 Find the next five numbers in the following number pattern. 1, 4, 9, 1, 6, 2, 5, 3, 6, 4, 9, 6, 4, 8, 1,___,___,___,___,___

REASONING 11 11, 12 12, 13

11 Jemima writes down the following number sequence: 7, 7, 7, 7, 7, 7, 7,… a 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 b 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 c 1 + 2 + 3 + 4 + 5 +… + 67 + 68 + 69 + 70 d 5 + 8 + 11 + 14 + 17 + 20 + 23 + 26 + 29 + 32 + 35 + 38

Her friend Peta declares that this is not really a number pattern. Jemima defends her number pattern, stating that it is most definitely a number pattern as it has a common difference and also has a common ratio. What are the common difference and the common ratio for the number sequence above? Do you agree with Jemima or Peta?

12 Find the sum for each of the following number sequences.

13 The great handshake problem

There are a certain number of people in a room and they must all shake one another’s hand. How many handshakes will there be if there are: a 3 people in the room? b 5 people in the room? c 10 people in the room? d 24 people in a classroom? e n people in the room?

Diagram showing the possible handshakes with five people

ENRICHMENT: What number am I? – – 14

14 Read the following clues to work out the mystery number.

a I have three digits.

I am divisible by 5

I am odd.

The product of my digits is 15.

The sum of my digits is less than 10.

I am less than 12 × 12 b I have three digits.

The sum of my digits is 12 c I have three digits.

My digits are all even.

My digits are all different.

I am divisible by 4.

The sum of my units and tens digits equals my hundreds digit.

I am odd and divisible by 5 and 9

The product of my digits is 180

The sum of my digits is less than 20.

I am greater than 302 d Make up two of your own mystery number puzzles and submit your clues to your teacher.