# make a sum with cards

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.

• Can you specify what the allowed actions are, please? Can we for example form the number 9876543210? – hexomino Aug 12 '18 at 9:43
• A single number is not a sum. You must have one or more plus signs. – mau Aug 12 '18 at 9:51
• answer is hidden in this answer of this question [ here](puzzling.stackexchange.com/questions/53684/…). – Oray Aug 12 '18 at 10:14
• @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. – xhienne Aug 12 '18 at 11:24
• @xhienne i did not refer that part, just gave an answer from another perspective :) no other intention. – Oray Aug 12 '18 at 11:25

## 2 Answers

Two solutions in 9 cards and 1 sum:

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

• I did not think that a carry was not necessary to reach 1000+ in the sum :-) – mau Aug 12 '18 at 10:45

As far as I understand the rules, the maximum sum would be :

987654310 + 2 = 987654312

• You don't have two copies of the cards, and besides there is no 1. – mau Aug 12 '18 at 17:21
• 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. – Evargalo Aug 13 '18 at 7:56