Advanced Pigeonhole Principle Quiz � Complex Logical Problems (MP.1, MP.3)

1) What is the minimum number of people required to ensure at least 10 share a birthday day of the week?

64

63

62

70

7(10−1)+1=647(10−1)+1 = 647(10−1)+1=64

Explanation

7(10−1)+1=647(10−1)+1 = 647(10−1)+1=64

2) How many marbles must be placed into 15 jars to guarantee one jar contains at least 12 marbles?

166

165

167

170

15(12−1)+1=16615(12−1)+1 = 16615(12−1)+1=166

Explanation

15(12−1)+1=16615(12−1)+1 = 16615(12−1)+1=166

3) If 121 items are placed in 12 boxes, at least how many must be in one box?

9

10

11

12

⌈121/12⌉=⌈10.08...⌉=11\lceil 121/12 \rceil = \lceil 10.08...\rceil = 11⌈121/12⌉=⌈10.08...⌉=11

Explanation

⌈121/12⌉=⌈10.08...⌉=11\lceil 121/12 \rceil = \lceil 10.08...\rceil = 11⌈121/12⌉=⌈10.08...⌉=11

4) If 500 objects are distributed into 37 boxes, what is the minimum in one box?

13

14

15

16

⌈500/37⌉=⌈13.51⌉=14\lceil 500/37 \rceil = \lceil 13.51 \rceil = 14⌈500/37⌉=⌈13.51⌉=14

Explanation

⌈500/37⌉=⌈13.51⌉=14\lceil 500/37 \rceil = \lceil 13.51 \rceil = 14⌈500/37⌉=⌈13.51⌉=14

5) What is the least number of cards to guarantee at least 6 of the same suit? (4 suits)

21

22

23

24

4(6−1)+1=234(6−1)+1 = 234(6−1)+1=23

Explanation

4(6−1)+1=234(6−1)+1 = 234(6−1)+1=23

6) A competition has 250 participants divided among 11 teams. Minimum guaranteed in one team?

26

24

23

25

⌈250/11⌉=⌈22.72...⌉=25\lceil 250/11 \rceil = \lceil 22.72... \rceil = 25⌈250/11⌉=⌈22.72...⌉=25

Explanation

⌈250/11⌉=⌈22.72...⌉=25\lceil 250/11 \rceil = \lceil 22.72... \rceil = 25⌈250/11⌉=⌈22.72...⌉=25

7) How many candies must be distributed among 20 kids to guarantee one kid gets at least 8 candies?

141

140

139

150

20(8−1)+1=14120(8−1)+1 = 14120(8−1)+1=141

Explanation

20(8−1)+1=14120(8−1)+1 = 14120(8−1)+1=141

8) If 333 beads are placed into 17 containers, the minimum beads in one container is

20

19

21

18

⌈333/17⌉=⌈19.58...⌉=20\lceil 333/17 \rceil = \lceil 19.58...\rceil = 20⌈333/17⌉=⌈19.58...⌉=20

Explanation

⌈333/17⌉=⌈19.58...⌉=20\lceil 333/17 \rceil = \lceil 19.58...\rceil = 20⌈333/17⌉=⌈19.58...⌉=20

9) How many people are needed to ensure at least 15 share a birth month?

168

170

160

169

12(15−1)+1=16912(15−1)+1 = 16912(15−1)+1=169

Explanation

12(15−1)+1=16912(15−1)+1 = 16912(15−1)+1=169

10) If 75 objects are placed into 8 boxes, the minimum in one box is

10

9

8

11

⌈75/8⌉=⌈9.375⌉=10\lceil 75/8 \rceil = \lceil 9.375 \rceil = 10⌈75/8⌉=⌈9.375⌉=10

Explanation

⌈75/8⌉=⌈9.375⌉=10\lceil 75/8 \rceil = \lceil 9.375 \rceil = 10⌈75/8⌉=⌈9.375⌉=10

Generalized Pigeonhole Principle — Harder Reasoning

1) What is the minimum number of people required to ensure at least 10 share a birthday day of the week?

2)

What first name or nickname would you like us to use?

2) How many marbles must be placed into 15 jars to guarantee one jar contains at least 12 marbles?

3) If 121 items are placed in 12 boxes, at least how many must be in one box?

4) If 500 objects are distributed into 37 boxes, what is the minimum in one box?

5) What is the least number of cards to guarantee at least 6 of the same suit? (4 suits)

6) A competition has 250 participants divided among 11 teams. Minimum guaranteed in one team?

7) How many candies must be distributed among 20 kids to guarantee one kid gets at least 8 candies?

8) If 333 beads are placed into 17 containers, the minimum beads in one container is

9) How many people are needed to ensure at least 15 share a birth month?

10) If 75 objects are placed into 8 boxes, the minimum in one box is