The problem below (Moscow Puzzles #313) can be solved in more than 4 ways,
(each d1 by itself) - using different approaches.
Find the number t and the digit represented by k in:
List your ways of solving it.
1. Trial and error:
Try all 10 possible values of k, either manually with a calculator, with a graphing calculator's table facility, or a spreadsheet, specifying:
a) sqrt(492004 + 100*k)/3 - 230
b) sqrt((492004 + 100*k)/9) - 230
to find the value of t that is integral:
so k is 8 and t is 4.
2. More direct:
Take the square root of 492004 and divide by 3. The result is the same 3.809989331318178 seen above; but recognize that the small change that any k would make (the 4th significant figure) is not going to change the result much, so assume the value of t is 4, the next higher digit. Then take [3*(230+4)]^2 verifying that all the given digits match the RHS and k turns out to be 8.
Similarly you could have chosen a starting middle value for k, such as 4 or 5, instead of zero, and likewise found the best digit for t is 4 and proceed from there.
3. Trial and error in the other direction:
Try the LHS with different values for t and see which match the given digits on the RHS. This has the disadvantage of not knowing the approximate size of t--not even that it's necessarily a 1-digit number, so an automated method would be a good choice. But you'd quickly see that method 2 above would be a better choice, as you'd want to know the approximate size of t at least.
Posted by Charlie
on 2017-12-21 11:31:11