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
Maury: 7847
Jaypee: 11847
Derrick: 9846
"Everyone except one is wrong" Ned told the gathering.
Who was it and how did Ned know?
All such sums are divisible by 11.
Call the number abcd.
The sum of abcd and dabc is:
= 1100a + 110b + 11c + 1001d
= 11(100a + 10b + c + 91d)
Using a divisibility test for 11 on each of the four numbers shows that only Jaypee's answer is divisible by 11.
(sum the digits in odd positions, sum the digits in even positions, if the difference of the two sums is divisible by 11, then the original number is divisible by 11).
|
|
Posted by Larry
on 2023-09-02 08:50:18 |
Analytic solution
