Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 A bag holds counters in 4 different colours. What is the smallest number that must be taken to be sure of two the same colour?
Show worked solution
Four could be one of each colour, so the fifth is forced to repeat: 5.
2 A drawer holds 10 black, 10 red and 10 blue socks. Write the most socks you could take while still having no matching pair, and the smallest number that guarantees a pair.
Show worked solution
Three socks — one of each colour — can avoid a pair (3), so 4 guarantees one.
3 A jar holds beads in 6 colours. How many must be taken to be sure of two the same colour?
Show worked solution
6 could all be different, so 7 forces a repeat.
Level 2 · Core
4 A drawer holds 10 black, 10 red and 10 blue socks. What is the smallest number that must be taken to be sure of having at least one BLUE sock?
Show worked solution
10 black and 10 red make 20 socks with no blue, so the 21st is forced to be blue: 21.
5 A drawer holds 8 white and 8 grey socks. Write the smallest number to be sure of a matching pair, and the smallest number to be sure of a GREY pair.
Show worked solution
Two colours means 3 guarantees a pair. For grey, 8 white could come first, then 2 grey: 8 + 2 = 10.
6 A box holds 12 red, 12 green and 12 yellow cubes. How many must be taken to be sure of a pair of each colour?
Show worked solution
12 + 12 = 24 gives two pairs but no third colour, so 2 more are forced: 26.
Level 3 · Challenge
7 A drawer holds 10 black, 10 red and 10 blue socks.1 22 socks guarantee a red pair.
2 22 socks guarantee a pair of every colour.
3 Both answers are 22 for the same reason.
Which statements are correct?
2 22 socks guarantee a pair of every colour.
3 Both answers are 22 for the same reason.
Which statements are correct?
Show worked solution
Both are 22 (1 ✓, 2 ✓), but by different runs: the red-pair run is 10 black + 10 blue + 2 red, while the every-colour run is 10 black + 10 red + 2 blue (3 ✗). 1 and 2.
8 A drawer holds 10 socks in each of 4 colours. Write the smallest number to be sure of any matching pair, and the smallest number to be sure of a pair of one named colour.
Show worked solution
Four colours means 5 guarantees a pair. For a named colour, 3 × 10 = 30 others could come first, then 2: 32.
9 A bag holds 7 red and 7 blue marbles. How many must be taken to be sure of having 3 of the same colour?
Show worked solution
Two of each colour is 4 marbles with no set of three, so the 5th forces a third of some colour: 5.