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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Simple to simplify?
This is a lovely question that I was emailed by brilliant.org If you haven't seen that site then do go there. I suggest signing up for the free access and having fun exploring some of their frankly brilliant problems. This one involves some nice techniques and will allow you to delve into different A-level maths ideas.
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