perplexus.info :: Numbers : Integers with Happy, Healthy Babies

Integers with Happy, Healthy Babies (Posted on 2023-01-26)

An integer has a baby if its square root appears inside it.
To be inside, there must be at least one parental digit on either side of the baby.
A baby is happy if it is perfectly centered within its parent integer, ie the same number of digits to its left and to its right.
A baby is healthy if the baby does not contain any zeros.

For example, the square root of 62500 is 250, so 62500 has a happy, but unhealthy baby.
The square root of 214651801 is 14651, so 214651801 has a healthy but unhappy baby. This baby has one digit to its left, but three digits to its right.

Find the first 4 integers with happy, healthy babies.

No Solution Yet Submitted by Larry

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computer solution

Comment 1 of 1

clearvars,clc

for n=uint64(1):uint64(90000000)

ns=string(n);sqs=string(n^2);

charn=char(ns);

charsq=char(sqs);

ix=strfind(sqs,ns);

diff=length(charsq)-length(charn);

if mod(diff,2)==0

for j=1:length(ix)

if ix(j)==diff/2+1

if length(strfind(ns,'0'))==0

fprintf('%10d %20d\n',n, n^2)

end

finds

     Baby
   (square         Integer with
     root)          H, H. Baby  
      3792             14379264
    495475         245495475625
    971582         943971582724
  66952741     4482669527413081

Posted by Charlie on 2023-01-26 10:32:05

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