Problem involving sum-of-digits
A problem to solve:
Let a be the
answer to this problem, where a is a
positive integer, and let b be the
sum of its digits. Calculate 2a – 2b.
Work out x
How did you do it?
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Let a be a 2 digit number and equal to 10x + y where 10x is the digit in the tens column and y is the digit in the units column. That means that b=x+y. Therefore 2a-2b is 2(10x+y) - 2(x+y) so 18x. We can check if it works: if a is 17 then b is 8 and x is 1 and y is 7. So 2a-2b is 34-16 which is 18. If we enter x=1 into 18x we get 18 which is the same. Therefore 2a-2b is 18x where x is the digit in the tens column. I haven't tried this with a three digit number but I think the answer will be 198x where x is the digit in the hundreds column
ReplyDeleteYou have used some neat ideas here.
DeleteI don't want to spoil the fun for others, so I will only say at the moment that there are alternative ways to do this too. And I disagree about three digits!
my bad, the three digit one should be 198x + 18y where x is the number in the hundreds column and y is thenumber in the tens column
Delete