A 2-Digit number is squared. When this 2-digit number is reversed
and squared, the difference between the squares is also a square.
What is the 2-digit number?
Stage: 4 Challenge Level:
Well done to Jim sent us his
The trick to solving this problem is to work systemticlly. The 8
weight can be placed on either the end or the inner point, and it
is symetrical so we only have to look at on side.
If the 8 is on the end the arrangements to consider are:
If the 8 is on an inner attachment point we need to consider:
I them tried to find the balance points, and found they were in the
central interval except for 8241, 8412 and 8412. I found that 4821
and 8142 produce a balance point at one of the inner attachment
For 8241, and 8412 the bar needs weight 4/3, for 8421, 8/3 is
required. So the bar must be at least 8/3 in weight for all
arrangments to have balance points in the central interval.
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