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What is the minimum number of times you must throw three fair six-sided dice to ensure that the same sum is rolled twice?

 Jun 1, 2021
 #1
avatar+2207 
+2

You can have 16 (3-18) total sums. 

So worse case scenerio, you roll all 16 once, meaning that you have to roll 17 time to ensure that the same sum is rolled. 

 

=^._.^=

 Jun 1, 2021
 #2
avatar+121055 
+2

We can't say  what the  minimum number  might be  ( we COULD  get  the  same sum on two consecutive rolls)

 

We  have    16  different   outcomes

 

However, by the pigeonhole principle, we can  guarantee  that  we will get the SAME sum (at least once) after a maximum of   16  rolls after  the  initial result......so 17  total rolls

 

 

cool cool cool

 Jun 1, 2021
 #3
avatar+91 
+2

Thank you Cphill

 Jun 1, 2021

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