perplexus.info :: Numbers : BCCDEFGGB and Perfect Square

BCCDEFGGB and Perfect Square (Posted on 2023-04-10)

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.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

EF= 16, 25, 36, 49, 64, 81.
GGB = 225, 441
Then, by calculator, we have:
EFGGB is a perfect square, whenever:
EFGGB = 81225
Then, we have: B=5, giving:
BCCB =5776
Therefore, BCCDEFGGB = 577681225, the square root of which is readily found to be 24035, by means of a calculator.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
calculator+pen+paper	xdog	2023-04-10 17:31:42
Computer Solution	Larry	2023-04-10 14:40:57
computer solution	Charlie	2023-04-10 14:30:16

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