ReasoningAges 13-15

Worst-case pigeonhole guarantee

Use worst-case distribution reasoning to find the minimum number of picks needed to guarantee a match. Review suitability for your learners before teaching.

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Age band:Ages 13-15 Ages 16-18

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Worksheet StudioPractice pack · Ages 13-15

Worst-case pigeonhole guarantee

Take your time. Show your thinking.

1. A drawer contains socks in 6 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 3 socks of the same colour?
6 · 3 s · Worst-case pigeonhole guar…
2. A drawer contains socks in 5 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 6 socks of the same colour?
5 · 6 s · Worst-case pigeonhole guar…
3. A drawer contains socks in 3 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 5 socks of the same colour?
3 · 5 s · Worst-case pigeonhole guar…
4. A drawer contains socks in 2 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 6 socks of the same colour?
2 · 6 s · Worst-case pigeonhole guar…
5. A drawer contains socks in 3 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 6 socks of the same colour?
3 · 6 s · Worst-case pigeonhole guar…
6. A drawer contains socks in 8 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 5 socks of the same colour?
8 · 5 s · Worst-case pigeonhole guar…
7. A drawer contains socks in 6 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 6 socks of the same colour?
6 · 6 s · Worst-case pigeonhole guar…
8. A drawer contains socks in 5 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 4 socks of the same colour?
5 · 4 s · Worst-case pigeonhole guar…
9. A drawer contains socks in 3 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 4 socks of the same colour?
3 · 4 s · Worst-case pigeonhole guar…
10. A drawer contains socks in 7 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 2 socks of the same colour?
7 · 2 s · Worst-case pigeonhole guar…
11. A drawer contains socks in 7 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 3 socks of the same colour?
7 · 3 s · Worst-case pigeonhole guar…
12. A drawer contains socks in 4 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 4 socks of the same colour?
4 · 4 s · Worst-case pigeonhole guar…

12 questions · Seed 48 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Worst-case pigeonhole guarantee

Answers and reasoning. Review before teaching.

1. A drawer contains socks in 6 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 3 socks of the same colour?
13
In the worst case you could draw 2 of each of the 6 colours (12 socks). Drawing 1 more (13 in total) guarantees 3 of one colour.
2. A drawer contains socks in 5 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 6 socks of the same colour?
26
In the worst case you could draw 5 of each of the 5 colours (25 socks). Drawing 1 more (26 in total) guarantees 6 of one colour.
3. A drawer contains socks in 3 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 5 socks of the same colour?
13
In the worst case you could draw 4 of each of the 3 colours (12 socks). Drawing 1 more (13 in total) guarantees 5 of one colour.
4. A drawer contains socks in 2 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 6 socks of the same colour?
11
In the worst case you could draw 5 of each of the 2 colours (10 socks). Drawing 1 more (11 in total) guarantees 6 of one colour.
5. A drawer contains socks in 3 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 6 socks of the same colour?
16
In the worst case you could draw 5 of each of the 3 colours (15 socks). Drawing 1 more (16 in total) guarantees 6 of one colour.
6. A drawer contains socks in 8 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 5 socks of the same colour?
33
In the worst case you could draw 4 of each of the 8 colours (32 socks). Drawing 1 more (33 in total) guarantees 5 of one colour.
7. A drawer contains socks in 6 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 6 socks of the same colour?
31
In the worst case you could draw 5 of each of the 6 colours (30 socks). Drawing 1 more (31 in total) guarantees 6 of one colour.
8. A drawer contains socks in 5 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 4 socks of the same colour?
16
In the worst case you could draw 3 of each of the 5 colours (15 socks). Drawing 1 more (16 in total) guarantees 4 of one colour.
9. A drawer contains socks in 3 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 4 socks of the same colour?
10
In the worst case you could draw 3 of each of the 3 colours (9 socks). Drawing 1 more (10 in total) guarantees 4 of one colour.
10. A drawer contains socks in 7 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 2 socks of the same colour?
8
In the worst case you could draw 1 of each of the 7 colours (7 socks). Drawing 1 more (8 in total) guarantees 2 of one colour.
11. A drawer contains socks in 7 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 3 socks of the same colour?
15
In the worst case you could draw 2 of each of the 7 colours (14 socks). Drawing 1 more (15 in total) guarantees 3 of one colour.
12. A drawer contains socks in 4 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 4 socks of the same colour?
13
In the worst case you could draw 3 of each of the 4 colours (12 socks). Drawing 1 more (13 in total) guarantees 4 of one colour.

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Worst-case pigeonhole guarantee

Take your time. Show your thinking.

1. A drawer contains socks in 6 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 3 socks of the same colour?
6 · 3 s · Worst-case pigeonhole guar…
2. A drawer contains socks in 5 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 6 socks of the same colour?
5 · 6 s · Worst-case pigeonhole guar…
3. A drawer contains socks in 3 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 5 socks of the same colour?
3 · 5 s · Worst-case pigeonhole guar…
4. A drawer contains socks in 2 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 6 socks of the same colour?
2 · 6 s · Worst-case pigeonhole guar…
5. A drawer contains socks in 3 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 6 socks of the same colour?
3 · 6 s · Worst-case pigeonhole guar…
6. A drawer contains socks in 8 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 5 socks of the same colour?
8 · 5 s · Worst-case pigeonhole guar…
7. A drawer contains socks in 6 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 6 socks of the same colour?
6 · 6 s · Worst-case pigeonhole guar…
8. A drawer contains socks in 5 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 4 socks of the same colour?
5 · 4 s · Worst-case pigeonhole guar…
9. A drawer contains socks in 3 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 4 socks of the same colour?
3 · 4 s · Worst-case pigeonhole guar…
10. A drawer contains socks in 7 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 2 socks of the same colour?
7 · 2 s · Worst-case pigeonhole guar…
11. A drawer contains socks in 7 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 3 socks of the same colour?
7 · 3 s · Worst-case pigeonhole guar…
12. A drawer contains socks in 4 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 4 socks of the same colour?
4 · 4 s · Worst-case pigeonhole guar…

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Worst-case pigeonhole guarantee

Answers and reasoning. Review before teaching.

1. A drawer contains socks in 6 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 3 socks of the same colour?
13
In the worst case you could draw 2 of each of the 6 colours (12 socks). Drawing 1 more (13 in total) guarantees 3 of one colour.
2. A drawer contains socks in 5 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 6 socks of the same colour?
26
In the worst case you could draw 5 of each of the 5 colours (25 socks). Drawing 1 more (26 in total) guarantees 6 of one colour.
3. A drawer contains socks in 3 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 5 socks of the same colour?
13
In the worst case you could draw 4 of each of the 3 colours (12 socks). Drawing 1 more (13 in total) guarantees 5 of one colour.
4. A drawer contains socks in 2 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 6 socks of the same colour?
11
In the worst case you could draw 5 of each of the 2 colours (10 socks). Drawing 1 more (11 in total) guarantees 6 of one colour.
5. A drawer contains socks in 3 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 6 socks of the same colour?
16
In the worst case you could draw 5 of each of the 3 colours (15 socks). Drawing 1 more (16 in total) guarantees 6 of one colour.
6. A drawer contains socks in 8 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 5 socks of the same colour?
33
In the worst case you could draw 4 of each of the 8 colours (32 socks). Drawing 1 more (33 in total) guarantees 5 of one colour.
7. A drawer contains socks in 6 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 6 socks of the same colour?
31
In the worst case you could draw 5 of each of the 6 colours (30 socks). Drawing 1 more (31 in total) guarantees 6 of one colour.
8. A drawer contains socks in 5 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 4 socks of the same colour?
16
In the worst case you could draw 3 of each of the 5 colours (15 socks). Drawing 1 more (16 in total) guarantees 4 of one colour.
9. A drawer contains socks in 3 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 4 socks of the same colour?
10
In the worst case you could draw 3 of each of the 3 colours (9 socks). Drawing 1 more (10 in total) guarantees 4 of one colour.
10. A drawer contains socks in 7 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 2 socks of the same colour?
8
In the worst case you could draw 1 of each of the 7 colours (7 socks). Drawing 1 more (8 in total) guarantees 2 of one colour.
11. A drawer contains socks in 7 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 3 socks of the same colour?
15
In the worst case you could draw 2 of each of the 7 colours (14 socks). Drawing 1 more (15 in total) guarantees 3 of one colour.
12. A drawer contains socks in 4 different colours. What is the minimum number of socks you must draw without looking to guarantee having at least 4 socks of the same colour?
13
In the worst case you could draw 3 of each of the 4 colours (12 socks). Drawing 1 more (13 in total) guarantees 4 of one colour.

12 questions · Seed 48 · Age guidance, not curriculum certification