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- Feb 14, 2012
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Consider the set of integers ${1000,1001,1002,...1998,1999,2000}$.
There are times when a pair of consecutive integers can be added without "carrying": $1213 + 1214$ requires no carrying, whereas $1217 + 1218$ does require carrying.
For how many pairs of consecutive integers is no carrying required when the two numbers are added?
There are times when a pair of consecutive integers can be added without "carrying": $1213 + 1214$ requires no carrying, whereas $1217 + 1218$ does require carrying.
For how many pairs of consecutive integers is no carrying required when the two numbers are added?