# How many numbers between 100 and 999 are there in which the middle digit equals the sum of the other two digits? For the number 385, the middle digit equals the sum of the other two digits (8=3+5).

To find numbers between 100 and 999 with this same property, we perform the following calculations. Note that zero as the middle digit is impossible.

If the middle digit is 1, then the number will be 110 (1=1+0).

If the middle digit is 2, then the numbers will be 121 (2=1+1)and 220 (2=2+0).

If the middle digit is 3, then the numbers will be 132 (3=1+2), 231 (3=2+1), and 330 (3=3+0).

If the middle digit is 4, then the numbers will be 143 (4=1+3), 242 (4=2+2), 341 (4=3+1), and 440 (4=4+0).

If the middle digit is 5, then the numbers will be 154, 253, 352, 451, and 550.

If the middle digit is 6, then the numbers will be 165, 264, 363, 462, 561, and 660.

If the middle digit is 7, then the numbers will be 176, 275, 374, 473, 572, 671, and 770.

If the middle digit is 8, then the numbers will be 187, 286, 385, 484, 583, 682, 781, and 880.

if the middle digit is 9, then the numbers will be 198, 297, 396, 495, 594, 693, 792, 891, and 990.

In all, there are 45 numbers between 100 and 999 that have the property described.

Last Reviewed by eNotes Editorial on