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?

Guest Jul 23, 2022

#2**+1 **

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

CPhill Jul 23, 2022