Ned asked each of his 4 children to think of a 4-digit number.
"Now transfer the last digit to the front and add the new number to the old one.
For example, 1234 + 4123 = 5357.
Now tell me the results."

The results were told by each of the four children as follows:

Barry: 2348
Mary: 7847
Jaypee: 11847
Darla: 9846

"Only one of you gave me the correct sum" Ned told the gathering.
Who was it and how did Ned know?


Solution to the Problem:


Only Jaypee's response is correct.

The sum of two such numbers is always divisible by 11.
Let the number be ABCD = 1000A + 100B + 10C + D

Then, placing the last digit to the front we have the number DABC = 1000D +100A + 10B + C

Then, ABCD + DABC = 1001D + 110A + 110B + 11C = 11(91D + 10A + 10B + C)

Now, Barry's response = 2348, which is NOT divisible by 11
Mary's response = 7847, which is NOT divisible by 11
Jaypee's response = 11847 = 11 * 1077
Darla's reponse = 9846, which is NOT divisible by 11

Hence, only Jaypee's response is accurate.


Correctly solved by:

1. Rob Miles Northbrook, Illinois, USA
2. Sudhir Bavdekar Mumbai, India
3. Davit Banana Istanbul, Turkey
4. Seth Cohen Concord, New Hampshire, USA
5. Carlos de Armas Barcelona City, Spain
6. Dr. Hari Kishan D.N. College,
Meerut, Uttar Pradesh, India
7. Ivy Joseph Pune, Maharashtra, India
8. Colin (Yowie) Bowey Beechworth, Victoria, Australia
9. Kamal Lohia Hisar, Haryana, India
10. Kelly Stubblefield Mobile, Alabama, USA