From International Mathematics Contest

How many 2007-digit numbers exist, in which every two-digit number composed of two sequential digits is divisible either by 17 or 23? A) 5 B) 6 C 7 D) 9 E) More than 9. We note that n=123….(n-1)n. If n!=(2^15) (3^6) *(5^3 )(7^2 )* 11 * 13, then n=? A) 13 B) 14 C) 15 D) 16 E) 17 please explain your answer! :)

#HelpMe!

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

9 is the answer for the first question Two digit multiples of 17 are 17,34,51,68,85 Two digit multiples of 23 are 23,46,69,92 We can make 2007 digit numbers by 234692.... These sequence can be start from 2,3,4,6 and 9 .Thus giving 5 chances. There is a 4 term extending sequence 8517 which can be merged to 6 (using 68).Thus we will get another 4 numbers which have last digit 8,5,1 and 7 respectively. Consisting of total 9 chances.

For 2nd question ,answer is 16 There is no 17 ,thus it cannot be 17!. 5^3 is present so it must be at least 15!. Checking the power of 2 we can confirm that it is 16!

muhammed shemeer k - 8 years, 2 months ago

From PLK

Zi Song Yeoh - 8 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$