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105
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avatar+336 

The expression $2\cdot 3 \cdot 4\cdot 5+1$ is equal to 121, since multiplication is carried out before addition. However, we can obtain values other than 121 for this expression if we are allowed to change it by inserting parentheses. For example, we can obtain 144 by writing\[ (2\cdot (3\cdot 4)) \cdot (5+1) = 144. \]In total, how many values can be obtained from the expression $2\cdot 3\cdot 4 \cdot 5 + 1$ by inserting parentheses? (Note that rearranging terms is not allowed, only inserting parentheses).

 

I am so confused, I do not know where to start.

 Mar 31, 2020
edited by nchang  Mar 31, 2020
edited by nchang  Mar 31, 2020
 #1
avatar+1956 
+1

Latex please? Sorry, but I cannot read this.

 Mar 31, 2020
 #2
avatar+111321 
+2

Here's what I get

 

2*3*4*5 +  1  = 121

 

2*3*4*(5 + 1)  =  24 * 6  = 144

 

2*3 * (4*5+ 1)  =  6 * 21  =  126

 

2*(3*4*5 + 1)   = 2 * 61  =   122

 

 

cool cool cool

 Mar 31, 2020
 #3
avatar+336 
+2

Thank you so much! Now, I just need to make them as cases and solve it. Thank you CPhill! smiley

 Mar 31, 2020
 #4
avatar+111321 
+1

LOL!!!....I just hope  that I found all of them!!!!!

 

cool cool cool

CPhill  Mar 31, 2020
 #5
avatar+336 
+2

Yes, you did! I got the answer right!

 Mar 31, 2020
 #6
avatar+336 
+2

I understand now, thank you!

 Mar 31, 2020
 #7
avatar+111321 
+1

Good!!!.....understanding is the  most important part...!!!

 

cool cool cool

CPhill  Mar 31, 2020

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