Consider the number 4
808
Notice: 4^2+8^2=80
i.e. the sum of the squares of this number's first and last digits equals the number obtained when the first and last digits are erased.
How many numbers with such feature exist below 10000?
Clearly, no leading zeroes.
(In reply to
Just counting (spoiler) by Steve Herman)
If the prohibition on leading zeros applies only to the 3 or 4digit number itself, and not the internal 2digit number, then there would be seven more, that is, 83, as the 1digit sums of squares would each account for both a 3digit and a 4digit number:
110 1010
121 1021
152 1052
240 2040
251 2051
282 2082
390 3090
Edited on July 17, 2017, 9:57 pm

Posted by Charlie
on 20170717 13:53:40 