A challenging digit pattern: numbers where the middle digit equals the sum of the outer digits, like 132 (1+2 = 3) and 264 (2+4 = 6). Among all three-digit numbers, how many have the middle digit equal to the sum of the first and last digits, where that sum is at most 9?

Question

Accepted Answer

45. First digit a is 1 to 9, last digit c is 0 to 9, with a + c <= 9 (middle = a+c, a single digit). For each a from 1 to 9, c ranges 0 to (9-a), giving (10-a) choices: 9+8+7+6+5+4+3+2+1 = 45.

A challenging digit pattern: numbers where the middle digit equals the sum of the outer digits, like 132 (1+2 = 3) and 264 (2+4 = 6).
Among all three-digit numbers, how many have the middle digit equal to the sum of the first and last digits, where that sum is at most 9?

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More Class 8 Patterns in Numbers practice

A challenging digit pattern: numbers where the middle digit equals the sum of the outer digits, like 132 (1+2 = 3) and 264 (2+4 = 6).Among all three-digit numbers, how many have the middle digit equal to the sum of the first and last digits, where that sum is at most 9?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 8 Patterns in Numbers practice

A challenging digit pattern: numbers where the middle digit equals the sum of the outer digits, like 132 (1+2 = 3) and 264 (2+4 = 6).
Among all three-digit numbers, how many have the middle digit equal to the sum of the first and last digits, where that sum is at most 9?