Make it absolutely certain.
These questions ask for a guarantee, not a lucky guess.
Ten questions, with the answers explained. Try them in your head, then open each answer when you're ready.
Play this quiz →QUESTION 1 / 10
A box holds cards labeled A or B. How many cards guarantee at least three with the same label?
- Three
- Four
- Six
- Five
Show answer & explanation+
Five
Four draws can split two and two. The fifth must make one label appear at least three times.
QUESTION 2 / 10
A bag has red, blue, and green tokens in unlimited supply. How many draws guarantee two of one color?
- Four
- Five
- Six
- Three
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Four
Three draws could give one of each color. The fourth must repeat a color.
QUESTION 3 / 10
Thirteen people enter a room. Must at least two share a birth month?
- No
- Only in a leap year
- Only if they are related
- Yes
Show answer & explanation+
Yes
There are twelve months. Thirteen people cannot all have different birth months.
QUESTION 4 / 10
Eight people each choose one weekday. Must two choose the same day?
- Yes
- Only if Sunday is excluded
- No
- Only if they choose randomly
Show answer & explanation+
Yes
Seven weekday options cannot hold eight choices without a repeat.
QUESTION 5 / 10
There are six red and four blue balls. How many unseen draws guarantee at least one red?
- Six
- Seven
- Five
- Four
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Five
In the worst case, the first four are all blue. The fifth must be red.
QUESTION 6 / 10
There are five red and two blue balls. How many unseen draws guarantee at least one blue?
- Three
- Four
- Five
- Six
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Six
The first five might all be red. The sixth must include a blue.
QUESTION 7 / 10
Five chairs seat at most one person each. Six people all need seats at once. Is five enough?
- Only in a circle
- Yes
- Only if they arrive early
- No
Show answer & explanation+
No
Six people need six separate seats under the stated rule.
QUESTION 8 / 10
Ten cards are numbered 1 through 10. How many must you take unseen to guarantee an odd number?
- Five
- Two
- Four
- Six
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Six
You could first draw all five even cards. A sixth card must be odd.
QUESTION 9 / 10
A bag has four red, four blue, and four green balls. How many draws guarantee three of one color?
- Seven
- Eight
- Six
- Five
Show answer & explanation+
Seven
You can draw two of each color in six draws. The seventh makes at least one color reach three.
QUESTION 10 / 10
Four boxes hold nine balls in total. Must at least one box contain three or more?
- No
- Only if the balls are identical
- Only if all boxes are used
- Yes
Show answer & explanation+
Yes
If each box held at most two, there could be at most eight balls.