# Number Properties Puzzle – Challenge 9

Do you enjoy exercising your brain? If so, then this puzzle is just for you. Let's see if you can solve this Math puzzle!

## Challenge:

How many positive integers less than 10,000 are there in which the sum of the digits equals 5?

A- 31

B- 51

C- 56

D- 62

E- 93

$11.99 Satisfied 123 Students The correct answer is C. We are looking for a number that the sum of its digits equals 5. Pairs possible: $$0,0,0,5; 1,4,0,0; 0,0,2,3; 1,3,1,0; 1,2,1,1; 0,1,2,2$$ Number of options for each pair: $$0,0,0,5 = \frac{4!}{3!} = \frac{4 ×3 ×2 ×1}{3 ×2 ×1} = 4 (5, 50, 500, 5,000)$$ $$1,4,0,0 = \frac{4!}{2!} = \frac{4 ×3 ×2 ×1}{2 ×1} = 12 (14, 41, 104, 140, 410, 401, 1004, 1040, 1400, 4001, 4010, 4100)$$ $$0,0,2,3 = \frac{4!}{2!} = \frac{4 ×3 ×2 ×1}{2 ×1} = 12 (23, 32, 230, 320, …)$$ $$1,3,1,0 = \frac{4!}{2!} =\frac{4 ×3 ×2 ×1}{2 ×1)} = 12 (113, 131, 311, 1013, …)$$ $$1,2,1,1 = \frac{4!}{3!} = \frac{4 ×3 ×2 ×1}{3 ×2 ×1} = 4 (1112, 1121, 1211, 2111)$$ $$0,1,2,2 = \frac{4!}{2! }=\frac{4 ×3 ×2 ×1}{2 ×1} = 12 (122, 212, 221, 1022, …)$$ Total: $$12 + 12 + 12 + 12 + 4 + 4 = 56$$ ### More math articles ### What people say about "Number Properties Puzzle - Challenge 9"? No one replied yet. X 30% OFF Limited time only! Save Over 30% SAVE$5

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