1. Four princesses each thought of a two-digit number, and Ivan thought of a four-digit number. After they wrote their numbers in a row in some order, the result was 132040530321. Find Ivan's number.
Solution. Let's go through the options. Option 1320 is not suitable because the remaining part of the long number is divided into fragments of two adjacent digits: 40, 53, 03, 21, and the fragment 03 is impossible, as it is not a two-digit number. Option 3204 is impossible due to the invalid fragment 05 (or the fragment 1 from a single digit). Option 2040 results in the impossible fragment 03. Option 0405 is not an option - it is a three-digit number. Option 4053 results in the impossible fragment 03. Option 0530 is impossible. Option 5303 is the only possible one, as option 3032 leads to a fragment of one digit 1.

Answer. 5303.

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