Year 8

# Gabriel's problem

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## Lesson details

### Key learning points

- In this lesson, you will learn about a famous maths problem called Gabriel's problem.

### Licence

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

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### 6 Questions

A sequence is defined as follows: Start with any positive integer value (𝑛). Each term is found from the previous term as follows: If the value is even, divide it by 2 (𝑛/2). If the value is odd, multiply it by 3 and add 1 (3𝑛+1).

Q2.

If the first term of the sequence is 30, what would the second term be?

100

60

91

Q3.

If the second term of the sequence is 30, what would could the first term be?

100

15

91

Q4.

Fill in the gap: The Collatz conjecture states: no matter the start number (𝑛), the sequence will always reach __________.

half of the start number

infinity

zero

Q5.

What is the first name of Mr Collatz?

Bob

Christian

Leonard

Q6.

In what year did Collatz make his conjecture?

1927

1997

2007

### 3 Questions

Q1.

Each blue box is the product of the 3 numbers in that row or column. All the questions refer to this picture below. First, what is the value in box A?

16

9

Q2.

What is the value in box B?

1

3

4

Q3.

Which of the following could be a value for C?

112

189

83