Consider three-digit numbers in which the middle digit equals the sum of the first and last digits. For example, in 132 the middle digit 3 = 1 + 2, and in 165 the middle digit 6 = 1 + 5. How many such three-digit numbers have first digit 1 (that is, of the form 1, m, last with m = 1 + last)?

Question

Accepted Answer

9. First digit 1, last digit d from 0 to 8 (so middle = 1 + d no more than 9). d = 0,1,...,8 gives 9 numbers: 110, 121, 132, ..., 198.

Consider three-digit numbers in which the middle digit equals the sum of the first and last digits.
For example, in 132 the middle digit 3 = 1 + 2, and in 165 the middle digit 6 = 1 + 5.
How many such three-digit numbers have first digit 1 (that is, of the form 1, m, last with m = 1 + last)?

Step-by-Step Solution

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More Class 6 Patterns and Rules practice

Consider three-digit numbers in which the middle digit equals the sum of the first and last digits.For example, in 132 the middle digit 3 = 1 + 2, and in 165 the middle digit 6 = 1 + 5.How many such three-digit numbers have first digit 1 (that is, of the form 1, m, last with m = 1 + last)?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 6 Patterns and Rules practice

Consider three-digit numbers in which the middle digit equals the sum of the first and last digits.
For example, in 132 the middle digit 3 = 1 + 2, and in 165 the middle digit 6 = 1 + 5.
How many such three-digit numbers have first digit 1 (that is, of the form 1, m, last with m = 1 + last)?