## Find the number of pairs of consecutive integers in the set {4000, 4001, 4002, …, 5000} such that no carrying is required when the two integ

Question

Find the number of pairs of consecutive integers in the set {4000, 4001, 4002, …, 5000} such that no carrying is required when the two integers are added. প্রতি

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3 weeks 2021-11-07T09:29:36+00:00 1 Answer 0 views 0

156

Step-by-step explanation:

The first of consecutive integers that can be added without a carry are ones that have 0, 1, 2, 3, 4 in any digit position. There are 5^3 = 125 such integers in the given range.

Additionally, a 9 in the rightmost digit position will give such a number if there is a 0-4 in the other two digit positions. For example, 4449 +4450 = 8899. There are 25 of these.

Further, a 9 in the first and second digit positions will give such a number if there is a 0-4 in the hundreds place. There are 5 of these.

Finally, 4999 +5000 = 9999 with no carry. This is the largest of the numbers of interest.

Hence the total number of the numbers of interest is 125 +25 +5 +1 = 156.