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Jae-ho’s special coin has the number 5 on one side and 6 on the other side.  Jae-ho flips the coin an unlimited number of times, and his score is determined by summing the numbers which appear on top. What is the greatest integer number of points that Jae-ho can never score?

 Jul 23, 2022
 #1
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The answer is 4.

 Jul 23, 2022
 #2
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He can score any number  ending in 0 (starting with 10)  with an even number (starting at 2)  of  "5" flips 

 

He can score any number ending in 1  (starting with 11) with an  odd number of "5" flips and one "6" flip

 

He can score  any number ending with 2 (starting with 12)  with an two "6" flips  and any even number  (starting at 0) of "5"  flips 

 

He can score any number ending in 3  (starting wih 23) with an 3 flips of "6" and an odd number  of "5" flips   (He cannot make  13)

 

He can score any number ending in 4 (starting with 24)  =  four "6" flips  and an even number (starting at 0) of "5" flips   (he cannot make 14)

 

He can score any number ending in 5  with  any  number of "5" flips starting at 1 

 

He can score any number ending in 6   (starting with 6) with one "6" flip and an even number (starting at 0) of "5" flips 

 

He can score any  number ending in 7 (starting at 17) with  two "6" flips and  an odd number of "5" flips 

 

He can score any number ending in 8  (starting at 18)  with 3 flips of 6 and any number of even flips (starting at 0) of "5" 

 

He can score any number ending in 9 (starting with 29) with 4 flips of "6" and any odd number of "5" flips

(He cannot make 19)

 

So....

The greatest integer that is  impossible for him to flip  is  19

 

cool cool cool

 Jul 23, 2022

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