NOTE: I added a new solution (see (e) below). Also, read the comments to see even more solutions. Thanks to Jonathan for pointing out my error in (d) of my results.
I'll get to that cryptic title in a moment (may be obvious to some)...
1. Remember the challenge problem I posted in the tribute to Martin Gardner a few days ago? Well, we rec'd several excellent replies and I have an additional response from a very sharp high schooler as well. Here was the problem:
Can you form 95 using each of the digits 5-2-2-1-0 exactly once? No restrictions on the arithmetic operations, parentheses, factorials, roots, logs, etc... You may combine the digits to form numerals like 12 or 120.
Mr. Lomas: 5! - (2+2)! - 1 - 0 Perhaps the most elegant since it uses the individual digits in the given order.
Robot Guy: (21-2)*5+0
Nate (high schooler): 120-5^2 Oh, the simplicity of that one! Combining digits is not the first way I thought of...
Mine so far:
(a) 102 - (5+2) Pretty simple but I wasn't thinking much of combining digits until I saw Nate's
(b) 120 -25 (Shameless plagiarism from Nate's but I couldn't resist!)
(c) (2^5)(2+1) - 0! (I posted this one already)
(d) 10^2 - 5 x (2 - 0!) (I knew there had to be a way using 100 - 5)
NOTE: JONATHAN POINTED OUT MY ERROR HERE. SEE COMMENTS.
(e) A new one: (2 + 2)! x (5-1) - 0! I felt I needed to atone for my error in (d)!
I suspect Mr. Lomas has even more! It was definitely the spirit of Martin Gardner at work here!
Keep these coming if you can find more. I'd like to see us get to 10 ways.
(2/3) egg per (hen⋅day) x 3 hens x 3 days = 6 eggs.
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