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Special Numbers (Posted on 2004-04-03) Difficulty: 2 of 5
There exists a number oddity with 3 different 4-digit numbers. One is 9801, where (98 + 01)^2 = 9801. It also works with 3025: (30+25)^2 = 3025.
What is the other number?
What is the smallest 6-digit number that would work?
(in other words, in a 6-digit number abcdef: abcdef=(abc+def)^2)

See The Solution Submitted by Victor Zapana    
Rating: 3.6667 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer solution | Comment 1 of 18

The program:

DEFDBL A-Z
CLS
FOR n = 1000 TO 9999
  n$ = RIGHT$(LTRIM$(STR$(n)), 4)
  a$ = LEFT$(n$, 2)
  b$ = RIGHT$(n$, 2)
  t = VAL(a$) + VAL(b$)
  IF t * t = n THEN PRINT n
NEXT
FOR n = 100000 TO 999999
  n$ = RIGHT$(LTRIM$(STR$(n)), 6)
  a$ = LEFT$(n$, 3)
  b$ = RIGHT$(n$, 3)
  t = VAL(a$) + VAL(b$)
  IF t * t = n THEN PRINT n
NEXT

finds

 2025
 3025
 9801
 494209
 998001


  Posted by Charlie on 2004-04-03 10:34:56
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