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A quadruple gift for the N.Y. (Posted on 2022-12-28) Difficulty: 4 of 5
All answers must contain the string 2023:
1. What is the smallest number written exactly with 7 digits?
2. What is the smallest integer using 11 digits i.e. all digits 0 to 9 and an extra digit 2?
3. Write down the smallest square s.t. each digit is present at least once.
4. Evaluate the quadruplet {a,b,c,d} of distinct non-negative integers, s.t. a*b+c+d=2023 and abcd is minimal.

The 1st solver is kindly requested to post at least 2 answers out of the set of four.

See The Solution Submitted by Ady TZIDON    
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Some Thoughts "Repaired" Official solution (spoiler) | Comment 7 of 8 |
I think the "repaired" official solution is a bit garbled and needs to be re-"repaired".

I propose:

1. Smallest positive number: 0.002023
    Smallest negative number -9992023
2. Smallest positive integer: 12023456789
    Smallest negative integer: -98765420231

Note that, as required, -98765420231 contains exactly one 3 and one 1, unlike the "repaired" official solution.  
Also, note that 0. is not an answer, because it does not include the string 2023. 

  Posted by Steve Herman on 2022-12-30 18:52:40
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