Representation of 3 with Three Equal Digits

Use operations of addition, subtraction, multiplication, division, square root, and the decimal point to make true the identities below.

3 by three digits problem

In other words, represent $3$ with three instances of each digit. For example $1+1+1=3.$

Solution


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    Solution

    $1+1+1=3$

    $2+2/2=3$

    $3+3-3=3\cdot 3/3=3$

    $4-4/4=3$

    $.5\cdot 5+.5=3$

    $.6\cdot 6-.6=3$

    $7/.7-7=3$

    $\sqrt{8+8/8}=3$

    $\sqrt{9}+\sqrt{9}-\sqrt{9}=3$

    It was observed by a 16 year old boy from Israel that there is an universal template that works for all non-zero decimal digits: $\displaystyle\sqrt{(X-.X)/.X}=3.$

    |Contact| |Front page| |Contents| |Up| |Arithmetic|

     

    Copyright © 1996 - 2013 Alexander Bogomolny

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