August 22, 2007
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Math puzzle (you won't thank me)
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3252 hit(s)
In my never-ending quest to purge old files, I ran across a little math puzzle that "entertained" us for a long time several jobs ago. I don't remember where this came from; perhaps it's well known in math-puzzle circles, dunno. (Not my world, that.) If this is old news to you, just move along. For the newly initiated, however, here's the deal ...
The challenge is to calculate every integer value between 0 and 100 using only the number 4.
Rules:- You may use only the digit 4.
- Important: You may use no more than four 4's.
- You may use (only) the following operators:
+ (addition)
- (subtraction)
x or * (multiplication)
/ (division)
√ (square root)
! (factorial)
n4 (exponent) new
n¯ (overbar to indicate repetition) new
- Decimal points are ok. (Ex:
.4) new
- Concatenation is ok. (Ex:
44) new
- You can combine the operators to create any (otherwise legal) expression. Parentheses are ok.
Update 24 Aug 05: Jason's diligent research has enabled us to expand the list of allowable operators, yay!
Some examples:0 = 4-4
1 = 4/4
2 = √4
...
14 = (4x4)-√4
...
24 = 4!
You get the idea. Getting some of the numbers between 0 and 100 this way takes some thinking. AFAIK, it is possible to get all 100 numbers. I don't have the evidence right at hand, tho.
Some more sort-of meta rules:- I'm going to discourage you from publishing the complete results in the comments. Please. Ok?[1]
- Similarly, I'm going to discourage you from asking about expressions for specific numbers. However, let's see how it goes.
Most importantly, of course:- Every once in a while, stop and do some actual work. :-)
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