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avatar+214 

Question 1) How many positive five-digit integers contain the digit grouping "24" at least once? For instance, 24380 and 24440 are two such integers to include, but 23480 and 42034 do not meet the restrictions.

 

Question 2) For how many positive values of n are both \(n\over2\) and 3n four-digit base 9 integers?

edited by aboslutelydestroying  Apr 8, 2024
 #1
avatar+20 
+1

1. Do this: \(\text{There are 5 available options: xxxxx.} \\\text{These are the possible combinations: 24xxx, x24xx, xx24x, and xxx24} \\\text{it follows that: } \\10\cdot10\cdot10=1000\\ 9\cdot10\cdot10-1=899\\ 9\cdot10\cdot10-1=899\\ 9\cdot10\cdot10-2=898\\ \text{The answer is } 3696\)

 Apr 8, 2024
 #2
avatar+214 
+1

That is not the correct answer, can you check your explanation again please? Thank yousmiley

 #3
avatar+128794 
+1

1.  Since we have the condition "at least once," then "24" could  also appear twice, as well ...so... I think we could also have

 

2424x     =    10

24x24     =    10

x2424   =        9

 

= 19  more added to   blueorange's answer

 

cool cool cool

 Apr 9, 2024

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