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Thursday, April 22, 2010

Four Fours!


Today we tried to make all fo the numbers from 1-20 using four (no more, no less) fours.  We were allowed to use all four operations, as well as parentheses, exponents and combining the fours to make 44.  A wide variety of solutions were found, but I have included some that I found on the "Four Fours" Wikipedia page.  I have added some other solutions, in grey, since we used exponents and didn't use decimals, square roots (√) or factorials (!). 

Here is a set of four fours solutions for the numbers 0 through 20, using typical rules. Some alternate solutions are listed here, although there are actually many more correct solutions


0 = 44 − 44 = 4 − 4 + 4 − 4 = 4 + 4 - 4 - 4 

1 = 44 ÷ 44 = 4 ÷ 4 + 4 − 4 = (44 − 44)!

2 = 4 ÷ 4 + 4 ÷ 4

3 = (4 + 4 + 4) ÷ 4

4 = 4 ×(4 − 4) + 4

5 = (4 × 4 + 4) ÷ 4

6 = 4 × 4 + 4 - 4 = 4 + 4 + 4 ÷ 4

7 = 44 ÷ 4 − 4 = 4 + 4 − (4 ÷ 4)

8 = 4 + 4.4 − .4 = 4 + 4 + 4 − 4

9 = 4 + 4 + 4 ÷ 4

10 = (44 − 4) / 4 = 44 ÷ 4.4 = 4 + √4 + √4 + √4

11 = 4 ÷ .4 + 4 ÷ 4 = 4^2 - (4 + 4 / 4)

12 = (44 + 4) ÷ 4 = 4^2 - 4 + 4 - 4

13 = 4! − 44 ÷ 4= (4 − .4) ÷ .4 + 4 = 4^2 - 4 -4 / 4

14 = 4 × (4 − .4) − .4 = 4 ÷ .4 + √4 + √4 = 4^2 - (4 + 4) /4

15 = 44 ÷ 4 + 4 = 4 × 4 − 4 ÷ 4

16 = .4 × (44 − 4) = 4 × 4 × 4 ÷ 4 = 4 + 4 + 4 + 4 = √4 × √4 × √4 × √4

17 = 4 × 4 + 4 ÷ 4

18 = 44 × .4 + .4 = 4 × 4 + 4 ÷ √4 = 4^2 + (4 + 4) / 4

19 = 4! − 4 − (4 ÷ 4)  = 4^2 + 4 - 4 / 4

20 = 4 × (4 ÷ 4 + 4)
 
If you really want to be amazed, check out this site... Up to 100!
 
And even more amazing...  This pdf file has values (some are skipped) all the way up to 39,970!!!!
 
I really hope that you enjoyed this challenge today!  Be on the lookout for pictures from today this evening!
 
-Miss K  :)

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