How many numbers?
Probability
Level
3
How many 3-digit numbers are there for which the sum of the digits of the number is 24?
Click Here for more from this set.
9
12
2
10
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Begin with the fact that 8 multiplied by 3 is 24. This should lead one to see the 888 is one of these numbers. But what other combinations are there? Increase or decrease each digit alternatively to keep the digit sum at 24. This experimentation while result in only three possible cases: 8 + 8 + 8 = 2 4 ; 9 + 9 + 6 = 2 4 ; 7 + 8 + 9 = 2 4 The first case is trivial and results in only one combination. The second case can be rearranged in 3 different ways. And the final case has 6 different ways in which it can be arranged.
Therefore there are ten cases in total.