Inspired by Pi Han Goh

Logic Level 2

1 2 3 4 \color{#3D99F6} 1 \quad \color{#20A900} 2 \quad \color{#D61F06} 3 \quad 4

By using only multiplication ( × ) (\times) , addition ( + ) (+) and parenthesis ( ) () , make the expression above as large as possible without concatenating the digits.

Inspiration .

40 36 28 24 25

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Abhay Tiwari by Abhay Tiwari , 28, India

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2 solutions

Rex Holmes
May 9, 2016

(1+2) X (3X4) = 36

1 Helpful 0 Interesting 0 Brilliant 0 Confused

( 1 + 2 ) ( 3 × 4 ) = 36 (1+2)(3\times 4) = \boxed{36}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

How can you prove that 36 36 is the maximum number we can create from the given conditions ?

Sabhrant Sachan - 5 years, 1 month ago

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The expression that is tried to find out uses only addition and multiplication and for it to be as great as possible since multiplication gives bigger results than addition for all expressions of 2 terms with the exception of those expressions that contain 1 and 0 it can be said that as there are 4 numbers which are increasing in their magnitude in order to achieve a maximum it will be necessary for multiplication to be used at least once such that a resulting number from the combination of two of them uses the most "powerful" operation possible somewhere in the expression. In this case it is however enough to observe that the operation in which 1 is implied is addition because this gives so to say an increase in the resulting value while multiplication wouldn't give any and that because afterwards will be used multiplication (that will increase the result of any of the anterior expressions more than would do addition) the maximum expression that can be obtained before using that multiplication will be either 2 or 2+1 in which case it is obvious that the second is greater.

A A - 5 years, 1 month ago

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Nice logic

Sabhrant Sachan - 5 years, 1 month ago

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@Sabhrant Sachan – Haha. Thanks.

A A - 5 years, 1 month ago

Check out all possibility, further there are only two operations, so this not the difficult task!

akash patalwanshi - 5 years, 1 month ago

lol. interesting question

Syed Hamza Khalid - 2 years, 11 months ago

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