Consider the number 4

**80**8

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.

Well, if we allowed 5 digit numbers, then there would be 90, one for each number from 10 to 99.

For instance, consider 65. 6^2 + 5^2 = 36+25 = 61, so the number is 6**61**5.

However, for some numbers 10a+b, a^2 + b^2 > 99.

The numbers with this feature are

86 and 68

87 and 78

88

95 and 59

96 and 69

97 and 79

98 and 89

99

Altogether there are 14 of these.

So, the requested answer is 90 - 14 = **76**.