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MATH / 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…

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problem

The expression 2⋅3⋅4⋅5+12\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⋅(3⋅4))⋅(5+1)=144. (2\cdot (3\cdot 4)) \cdot (5+1) = 144. In total, how many values can be obtained from the expression 2⋅3⋅4⋅5+12\cdot 3\cdot 4 \cdot 5 + 1 by inserting parentheses? (Note that rearranging terms is not allowed, only inserting parentheses).
Plain-text mathematical notation (without MathML)
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).
Original LaTeX notation
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).

level

Level 5

type

Prealgebra

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Source and history

task_id
f701b2d3-92ef-508e-b6c6-869ddcae9f5d
task_key
prealgebra--test--f701b2d3-92ef-508e-b6c6-869ddcae9f5d
task_revision_id
1
config / split
prealgebra / test

Official source

initial import