Failure of the pattern
If we have the pattern below, where the first two digits of the product increase by one each time:
60 x 60 = 3600
61 x 61 = 3721
.
.
.
Then, what is the first value over 61 for which this
augmentation cease to work?
The answer is 65.
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1 solution
Starting at 60 then, we can think of the series as (60+x)^2. By expanding we get 3600+120x+x^2. Now we have two Problems to worry: 120x and x^2 - the sum of both breaks the pattern [when larger than 100*(x+1)] . In this case the pattern breaks for x=5 already: 600+25 > 600.