use the digits 1, 2, 3, 4, 5 & mathematical operations

[DavidLeese]

Hello everyone,
I've been busy... again. I've been working on a new puzzle, which has a very similar framework to the first - with one change: you have to use the digits 1,2,3,4 and 5. The inclusion of 5 into the puzzle means that there's no need for decimals, although factorials are still permitted. I've managed to produce 1-200 using +-/* powers and factorials - no decimals.

My answers from 1-100 are here:
http://davechessgames.blogspot.com/2015/09/numbers-12345-from-1-to-200.html

and I'll get 101 to 200 up later this week (when time allows). Please feel free to check my calculations and see if you can provide more elegant solutions (there are bonus points for elegance as always). For example:
- can you provide a solution where the digits are used in ascending order, e.g. 78 = 123 - 45, or 81 = (12 * 3) + 45
- can you use the minimum number of functions; e.g. only one addition or subtraction

Thanks

David

 

[lookagain]

Using digits 1,2,3,4,5 once each and in ascending order,
represent all numbers from 1 to 200.

Allowed: brackets, concatenation, + - / * ^ !
NOTHING else!

Examples:
1^2345 = 1
1 + 23 - 4 + 5 = 25
1^23 * 4 + 5! = 124

I've got them all except 76, 158, 167 and 169.

Can anybody get them? I'm going nuts

• Thanks

\(\displaystyle 76 \ = \ (-1 + 2)3^4 \ - \ 5\)

\(\displaystyle 76 \ = \ (-1 \ + \ 2 \ + 3)(4! \ - \ 5)\)

\(\displaystyle 76 \ = \ (12/3)(4! \ - \ 5)\)

\(\displaystyle 76 \ = \ (-1*2 \ + \ 3!)(4! \ - \ 5)\)

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\(\displaystyle 158 \ = \ -12 \ + \ 34*5\)

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\(\displaystyle 167 \ = \ -1 \ - 2 \ + \ 34*5\)

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\(\displaystyle 169 \ = \ 1 \ - 2 \ + \ 34*5\)

\(\displaystyle 169 \ = \ -1^2 \ + \ 34*5\)