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Logic Level 2

$\large 2 \times 3 + 4 \times 5$

If we're allowed to add any number of pairs of parentheses to the mathematical expression above, then how many distinct resultant numbers can we make?

2 3 4 5 Countless Values

1 solution

Rishabh Jain
Mar 5, 2016

$\Large \color{#D61F06}{(}2 \times 3\color{#D61F06}{)}+ \color{#D61F06}{(}4 \times 5\color{#D61F06}{)}=\color{#302B94}{\boxed{\textbf{26}}}$ $\Large 2 \times\color{#D61F06}{(}3 + 4 \color{#D61F06}{)}\times 5=\color{#302B94}{\boxed{\textbf{70}}}$ $\Large 2 \times\color{#D61F06}{(} 3 + 4 \times 5\color{#D61F06}{)}=\Large \color{#302B94}{\boxed{\textbf{46}}}$ $\Large \color{#D61F06}{(}2 \times 3 + 4\color{#D61F06}{)}\times 5= \Large \color{#302B94}{\boxed{\textbf{50}}}\\$

i.e $\Large \boxed{\textbf 4}$ different values.

@Anish Harsha Can you confirm that you intend for only 1 pair of parenthesis to be added?

Note that in the first line, we don't need to add any parenthesis at all.

How do we know that we've reached all possible values?

Calvin Lin Staff - 5 years, 3 months ago

No ,any no.of one pairs of paranthesis .

Anish Harsha - 5 years, 3 months ago

Thanks. I see that a moderator has wrongly edited this problem. I've updated the problem statement.

Brilliant Mathematics Staff - 5 years, 3 months ago

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