A perfect square is represented by BCCDEFGGB, where each of the letters is denoted by a distinct nonzero digit.
Furthermore:
- Each of BCCD and EFGGB is a perfect square.
- Each of EF and GGB is a perfect square.
Determine the square root of the number represented by BCCDEFGGB.
Note: Computer program solutions are welcome but a semi-analytic (calculator+p&p) method is preferred.
I looked at BCCD first because of the doubled central digit and found:
35^2=1225
46^2=2116
65^2=4225
76^2=5776
83^2=6889
85^2=7225
GGB is square too and can't end in 2 or 7. Only 21^2=441 and 15^2=225 fit.
Then EF square appended to GGB is square and only 285^2=81225 works.
The final check shows 24035^2=577681225.
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Posted by xdog
on 2023-04-10 17:31:42 |
calculator+pen+paper
