perplexus.info :: Numbers : 3 and 4-digit numbers

3 and 4-digit numbers (Posted on 2017-07-17)

Consider the number 4808
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.

See The Solution Submitted by Ady TZIDON

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Just counting (spoiler)

| Comment 1 of 7

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 6615.

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

The numbers with this feature are

86 and 68

87 and 78

95 and 59

96 and 69

97 and 79

98 and 89

Altogether there are 14 of these.

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

Posted by Steve Herman on 2017-07-17 13:08:18

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