The number 201 is divided by a positive integer N. It is observed that the quotient, remainder and divisor (that is, N itself), but not necessarily in this order, are in geometric sequence.

What can N be?

FOR n = 1 TO 201
  q = INT(201 / n)
  r = 201 - q * n
  IF n * n = q * r OR q * q = n * r OR r * r = n * q THEN PRINT n, q, r
NEXT

n              q            r
12            16            9
16            12            9

as 12*16 + 9 = 201.

 

 

Posted by Charlie on 2006-11-09 14:02:37