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.
In other words, represent $3$ with three instances of each digit. For example $1+1+1=3.$
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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: $\displaystyle\sqrt{(X-.X)/.X}=3.$
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Copyright © 1996 - 2013 Alexander Bogomolny
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