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We define the digit sum of a non-negative integer to be the sum of its digits. For example, the digit sum of 123 is 1 + 2 + 3 = 6. Let n be a positive integer with n < 10. How many positive integers less than 1000 have digit sum equal to n?

First we should consider how many positive integers less than 100 have digit sum equal to n. The answer should be relatively straight forward for this - it is n+1.For example, if n = 3 then we can have 03,12...
RL
Answered by Ron L. • MAT tutor
6492 Views

How do I make x the subject of the formula?

5x+11=(y+2)/2 Best way to think about this is like its a normal equation where you're trying to find the value of x, just break it down into simple steps. The best thing to do first is to get rid of any frac...
IO
Answered by Isabelle O. • Maths tutor
12764 Views

How does a tsunami form and why do their waves increase in size as they approach the shore?

This question is initially asking for the understanding tsunami formation process. It would be useful to provide a brief definition of a tsunami, so the examiner knows you have a clear idea of what a tsunami...
AS
Answered by Alice S. • Geography tutor
4715 Views

I am producing work of a very high quality, but this is not reflected in my grades. Why?

It is very common for A-level Art students who produce work which displays outstanding quality and technical skill to feel that their abilities are not reflected by their grades. This problem arises when stu...
RM
Answered by Reuben M. • Art tutor
2408 Views

Where does integration by parts come from?

The best way to do well in maths, is to learn where things come from. Mastering the basics makes everything else much easier! To start, consider the product rule with two functions u(x) and v(x) (using dashe...
TM
Answered by Tom M. • Maths tutor
3563 Views