20230610, 00:45  #45 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
7×13×89 Posts 
40 = 5*(4+3+21)
41 = 5*(4+3+21) + 1 39 = 5*(4+3+21)  1 "using only the digits 5, 4, 3, 2, and 1, in that order." (No other digits are allowed, and they must appear in the specified order) "You may not change the order of the numbers" It does NOT state the digits must only appear once per value! But this is an unsatisfying solution. It leads to a general case where, for any arbitrarily large number > 14, one can simply pile on the needed number of ones to be summed after a leading sequence such as 5+4+3+2 (Or for that matter: Must they all 5 appear at least once? Is the number base required to be ten?) In base 30, 39 (base 30) = 99 (base 10)= 5*4*(3+2)  1 15=55+4+3+2+1 has a typo; 15 = 5+4+3+2+1. There are more results with multiple solutions, eg 31 = 5*4*3/2 + 1 Last fiddled with by kriesel on 20230610 at 01:05 
20230610, 00:51  #46 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
1AD1_{16} Posts 
It also doesn't say we can't invoke the magic wizard spell MakusUppumShittius to give any answer we desire. So let's use that and solve all the puzzles.
Such interpretations of itdoesn'tsayXsolet'suseX render all puzzles useless and boring. 
20230610, 14:55  #47  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
7×13×89 Posts 
Quote:
Quote:
If the puzzle was correctly written, specifying too completely would provide too obvious a hint: Use only the digits 5, 4, 3, 2, and 1, in that order, at least once each. Identifying unstated and mistaken assumptions and putting them aside is what may separate the student that gets full credit from the ones that get an A grade while missing some points. 39 = (55 + 44 ) / 3 + 3 + 2 + 1 uses only the digits 5, 4, 3, 2, and 1, in that order, but some more than once, and the only operators in the expression are ()/+. On the other hand, having a set of rules which make the assigned task impossible to complete is an abuse of authority: Use only the numbers 5, 4, 3, 2, and 1, in that order, exactly once each. Or if the puzzle is fair, the appearance of no solution is a sign of an undetected incorrect assumption about the rules. Last fiddled with by kriesel on 20230610 at 14:55 

20230610, 17:23  #48  
"Jacob"
Sep 2006
Brussels, Belgium
7×281 Posts 
Quote:
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The rest of your post is about another situation altogether : did you note that the questions leaves a possibility that a number can't be represented, and then goes as far as asking which they or it might be ? The solution to the puzzle, its point, is to find out that 39 can't be represented. But I agree the puzzle is not stated in a formal mathematical way : it should speak of numbers and not digits ; it is not digits that one can group with parentheses, but operations, otherwise it opens the way to concatenation ; it doesn't specify the base ; perhaps one should specify the set and define the operations used ; ... It should be possible to state this puzzle in such a way that only a very few can understand it ;) Last fiddled with by S485122 on 20230610 at 21:43 Reason: go > goes and two commas 

20230610, 17:28  #49 
"Bob Silverman"
Nov 2003
North of Boston
3×5×509 Posts 

20230610, 18:47  #50  
Jan 2021
California
5^{2}·23 Posts 
Quote:
Last fiddled with by slandrum on 20230610 at 18:48 

20230610, 18:54  #51 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
1101011010001_{2} Posts 

20230611, 14:32  #52 
Feb 2017
Nowhere
5·1,307 Posts 
In the present instance, the digits 1, 2, 3, 4, and 5 indicate a base of at least six. Since the numbers (in base ten) 1 to 38 can be represented under the rules, but 39 (base ten) can not, and 40 base nine is 36 base ten, we can say that ten is the smallest base for which there is a number less than 40 which is not representable.

20230726, 07:21  #53  
Romulan Interpreter
"name field"
Jun 2011
Thailand
2×5,179 Posts 
Quote:
However, I agree with RDS that concatenation should not be used, ESPECIALLY because the puzzle says "digits", putting 4 and 3 together to get 43 is, in my mind, clearly, an operation which is called "digit concatenation". 

20230726, 14:30  #54  
Feb 2017
Nowhere
5·1,307 Posts 
Quote:
Quote:


20230726, 17:21  #55 
Jan 2021
California
5^{2}·23 Posts 
It says to use the digits in order, not the numbers 5,4,3,2,1. My answer above uses the digits in order along with + and . It clearly fits within the stated instructions. Problems of this sort are often stated like this so that in order to answer them, you have to let go of an automatic assumption.
My answer above is not the only answer either. 5 * 4 * 3  21 also works. 
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