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Take the numbered diamond cards in a standard deck, that is those from 2 to 10. You may use some of them to form a sum: for example 23+45=68. What is the maximum result you may obtain? I hoped there was some way to obtain 10xy, but this seems not to be the case.

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  • $\begingroup$ Can you specify what the allowed actions are, please? Can we for example form the number 9876543210? $\endgroup$ – hexomino Aug 12 '18 at 9:43
  • $\begingroup$ A single number is not a sum. You must have one or more plus signs. $\endgroup$ – mau Aug 12 '18 at 9:51
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    $\begingroup$ answer is hidden in this answer of this question [ here](puzzling.stackexchange.com/questions/53684/…). $\endgroup$ – Oray Aug 12 '18 at 10:14
  • $\begingroup$ @Oray Here we are not limited to the sum of two numbers and each number is not limited to three digits. If you have a formal proof that 1098 is the biggest number we can get in this puzzle, I think this would make a very interesting answer. $\endgroup$ – xhienne Aug 12 '18 at 11:24
  • $\begingroup$ @xhienne i did not refer that part, just gave an answer from another perspective :) no other intention. $\endgroup$ – Oray Aug 12 '18 at 11:25
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Two solutions in 9 cards and 1 sum:

$623+475=1098$ and $746+352=1098$

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    $\begingroup$ I did not think that a carry was not necessary to reach 1000+ in the sum :-) $\endgroup$ – mau Aug 12 '18 at 10:45
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As far as I understand the rules, the maximum sum would be :

987654310 + 2 = 987654312

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  • $\begingroup$ You don't have two copies of the cards, and besides there is no 1. $\endgroup$ – mau Aug 12 '18 at 17:21
  • $\begingroup$ Oh I see the problem now. The way the question is formulated, I didn't undertand that the right hand side (the evaluation of the sum) has to be written with cards too. $\endgroup$ – Evargalo Aug 13 '18 at 7:56

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