Question

The expression 2· 3· 4· 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· (3· 4))· (5+1)=144.

In total, how many values can be obtained from the expression 2· 3· 4· 5+1 by inserting parentheses? (Note that rearranging terms is not allowed, only inserting parentheses).

Answer 1

The expression 2· 3· 4· 5+1 can yield 2 different values, 121 and 144, by inserting parentheses in all possible ways without rearranging the terms.

Step-by-step explanation:

The question is asking how many different values can be obtained from the expression 2· 3· 4· 5+1 by inserting parentheses. To find out the number of different results we can get, we will explore different ways to group the numbers with parentheses which will affect the order of operations. Here are all the possible groupings:

• (2· (3· (4· 5))) + 1
• ((2· 3)· (4· 5)) + 1
• ((2· (3· 4))· 5) + 1
• (2· 3· 4)· (5 + 1)
• 2· ((3· 4)· (5+1))
• 2· (3· (4 · (5+1)))

Calculating each of these will give us the respective values:

• 2· 3· 20 + 1 = 121
• 6· 20 + 1 = 121
• 24· 5 + 1 = 121
• 24· 6 = 144
• 2· 12· 6 = 144
• 2· 3· 24 = 144

As we can see, there are only two distinct values that are obtainable here: 121 and 144. So, there are 2 different values that can be obtained from the given expression by inserting parentheses.