The number of natural numbers, between 212 and 999, such that the sum of their digits is 1…

Question

The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is \_\_\_\_\_\_\_.

Answer: 64

Accepted Answer

$\begin{gathered} x \quad  y \quad  z \end{gathered}$

Let $x=2\Rightarrow y+z=13$

$(4,9),(5,8),(6,7),(7,6),(8,5),(9,4),	o 6$

Let $x=3	o y+z=12$

$(3,9),(4,8),\ldots \ldots ..,(9,3)	o 7$

Let $x=4	o y+z=11$

$(2,9),(3,8),\ldots \ldots \ldots ,(9,1)	o 9$

Let $x=5	o y+z=10$

$(1,9),(2,8),\ldots \ldots ..,(9,1)	o 10$

Let $x=6	o y+z=9$

$(0,9),(1,8),\ldots \ldots ..,(9,0)	o 9$

Let $x=7	o y+z=8$

$(0,9),(1,7),\ldots \ldots ..,(8,0)	o 9$

Let $x=8	o y+z=7$

$(0,7),(1,6),\ldots \ldots ..,(7,0)	o 8$

Let $x=9	o y+z=6$

$(0,6),(1,5),\ldots \ldots \ldots ,(6,0)	o 7$

Total $=6=7+8+9+10+9+8+7=64$

Solutions · 1