Digit mania
Number Theory
Level
2
What is the minimum number of digits obtained by multiplying 13 digit number and 6 digit number and 17 digit number? [13 digits X 6 digits X 17 digits]
35
33
34
31
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1 solution
"The minimum number of digits obtained by multiplying any TWO numbers is ONE LESS than the sum of the digits of the numbers taken into account."
i.e. if the numbers have digits a and b repectively[in number], then the minimum digits obtained will be = (a+b-1)
And Maximum =a+b
The reason why i highlighted TWO is because the operation must be performed on exactly TWO numbers first...
Now in this question we have a 13 digit and 6 digit number first,
So minimum digits obtained after their multiplication will be =13+6-1=18
And then after we've got an 18 digit number, multiplying it with our last 17 digit number will give a minimum of [ 18+17-1 = 34 ] digits.
Hope you find the question interesting..
Suggestion(s) and/or modification(s) in the explaination are welcome.