Professor Uchiha is purchasing a ticket for the Super 10 Lotto. The lotto number has ten digits, using the numerals 0 through 9, each numeral used once. The clerk asked what number he wanted to pick. Professor Uchiha handed the clerk a piece of paper with nine statements, saying "If you can correctly figure out the number, I will give you half of whatever I win." What is the number?
1) The sum of the middle four digits is a cube number.
2) The sum of the first five digits is a prime number.
3) The sum of the last five digits is a triangular number.
4) The sum of the digits in the odd positions is an odd number.
5) The sum of the middle two digits is a square number.
6) The difference between the 1st and 10th digits is two.
7) The difference between the 2nd and 9th digits is three.
8) The difference between the 3rd and 8th digits is four.
9) The numeral 4 is somewhere in the first five positions.
Question
itachi-san
Professor Uchiha is purchasing a ticket for the Super 10 Lotto. The lotto number has ten digits, using the numerals 0 through 9, each numeral used once. The clerk asked what number he wanted to pick. Professor Uchiha handed the clerk a piece of paper with nine statements, saying "If you can correctly figure out the number, I will give you half of whatever I win." What is the number?
1) The sum of the middle four digits is a cube number.
2) The sum of the first five digits is a prime number.
3) The sum of the last five digits is a triangular number.
4) The sum of the digits in the odd positions is an odd number.
5) The sum of the middle two digits is a square number.
6) The difference between the 1st and 10th digits is two.
7) The difference between the 2nd and 9th digits is three.
8) The difference between the 3rd and 8th digits is four.
9) The numeral 4 is somewhere in the first five positions.
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