Systematic listing

The Maths Habit

In how many different orders can 10 people stand in a queue?

3 628 800

Systematic
Working in a fixed order, so that nothing is missed and nothing is written twice.

257

257 275

What comes next?

ABC   ACB   BAC   … BCA

Which number is missing from the list?

12   13   21   23   31 32

Two of these cards make a 2 digit number.
0 cannot go first. How many can be made?

0467
3 × 3 = 9

Three cards show 1, 6 and 8.
List all the 3 digit numbers.

168
168186618681816861
Fix the first one. Change the rest in order.
How many?6

Three cards show 2, 4 and 7.
List all the 3 digit numbers.

247
247274427472724742
How many?6

Three cards show 1, 6 and 8.
List all the 3 digit numbers.

168
168186618681816861
Fix the first one. Change the rest in order.
How many?6

Three cards show 3, 5 and 9.
List all the 3 digit numbers.

359
359395539593935953
How many?6

Three cards show 1, 6 and 8.
List all the 3 digit numbers.

168
168186618681816861
Fix the first one. Change the rest in order.
How many?6

Three cards show 2, 5 and 6.
List all the 2 digit numbers.

256
252652566265
How many?6

Three cards show 1, 6 and 8.
List all the 3 digit numbers.

168
168186618681816861
Fix the first one. Change the rest in order.
How many?6

Three cards show A, R and T.
List all the ways to put them in a row.

ART
ARTATRRATRTATARTRA
How many?6

Three cards show 1, 6 and 8.
List all the 3 digit numbers.

168
168186618681816861
Fix the first one. Change the rest in order.
How many?6

Three cards show 2, 6 and 8.
List all the 3 digit numbers, largest first.

268
862826682628286268
How many?6

Two of Lena, Max, Noor and Oli are picked.
List all the possible pairs.

LMNO

A snack is one drink and one fruit.
List all the snacks.

Drink
WJM
Fruit
AB

Systematic listing worksheet, page 1

Systematic listing worksheet, page 2

Answer sheet

  1. A café has 4 mains and 3 desserts. Without listing them, how many different meals of one main and one dessert are there?

    4 × 3 = 12

  2. Four cards show 1, 2, 3 and 4. How many 4 digit numbers can be made using each card once?

    24

  1. Three cards show 2, 6 and 9. List all the 3 digit numbers you can make with them.

    269 296 629 692 926 962

  2. Two of Pia (P), Raj (R), Sol (S) and Tam (T) are picked. List all the possible pairs.

    PR PS PT RS RT ST

  3. Three cards show 0, 3 and 8. A number cannot start with 0. How many 3 digit numbers can be made?

    4
Exit tickets to print