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


Related material
Read more...

  • Funny Arithmetic
  • A single formula to express all numbers
  • Any Integer with Three 2s
  • Representation of numbers with a single 4. The rules and the possibilities
  • One 4, a story
  • Three 3's
  • Representation of numbers with three 4's
  • Representation of numbers with three 5's
  • Representation of numbers with four 3's
  • Representation of numbers with four 4's
  • Representation of numbers with four 5's
  • A problem of representing 4 by four identical digits
  • A problem of representing 6 by three identical digits
  • A 9's Fan's Clock
  • Make an Identity
  • Fun with numbers: place plus/minus signs between the digits
  • 24 with One Digit
  • |Contact| |Front page| |Contents| |Up| |Arithmetic| |Store|

     

    Copyright © 1996 - 2013 Alexander Bogomolny


    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| |Store|

     

    Copyright © 1996 - 2013 Alexander Bogomolny

     62035919

    Search by google: