Please reference attachment. See image for more information. |16 How many three-digit numbers are composed of three distinct digits such that one digit isthe average of the other two?(A) 96(B) 104(C) 112(D) 120(E) 256

Answered: How many three-digit numbers are…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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|16 How many three-digit numbers are composed of three distinct digits such that one digit is
the average of the other two?
(A) 96
(B) 104
(C) 112
(D) 120
(E) 256

Expert Solution

Step 1

If the “average” digit is 1, then the other two digits are 0 and 2. For example, 210.

If the “average” digit is 2, then the other two digits are 1 and 3 OR 0 and 4. For example, 321 and 420.

If the “average” digit is 3, then the other two digits are 2 and 4 OR 1 and 5 OR 0 and 6. For example, 432, 531 and 630.

If the “average” digit is 4, then the other two digits are 3 and 5 OR 2 and 6 OR 1 and 7 OR 0 and 8. For example, 543, 642, 741 and 840.

If the “average” digit is 5, then the other two digits are 4 and 6 OR 3 and 7 OR 2 and 8 OR 1 and 9. For example, 654, 753, 852 and 951.

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