Here is a numbered list of statements, some true, some false, which refer to a specific number (unique positive integer, base 10).
It just so happens that if a statement is true then its index number appears among the number's digits, and if a statement is false then its index number does not appear among the number's digits.
- The sum of the number's digits is a prime.
- The product of the number's digits is odd.
- Each of the number's digits is less than the next digit (if there is one).
- No two of the number's digits are equal.
- None of the number's digits is greater than 4.
- The number has fewer than 6 digits.
- The product of the number's digits is not divisible by 6.
- The number is even.
- No two of the number's digits differ by 1.
- At least one of the number's digits is equal to the sum of two other digits. (Any of the digits may be equal, as long as all 3 digits are distinct... for example: {2, 2, 4} or {2, 3, 5} )
Find the number.
Hai,
Number 23569 will be the solution
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<TD align=left width=316 height=20>0 The sum of the number's digits is a prime i.e., 2+3+5+6+9 = 25 is not a prime --- False</TD></TR></TBODY></TABLE>
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<TD align=left width=316 height=20>1 The product of the number's digits is odd.I.e., 2*3*5*6*9=1620 is not an odd --- False</TD></TR></TBODY></TABLE>
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<TD align=left width=316 height=20>2 Each of the number's digits is less than the next digit (if there is one). ---- True</TD></TR></TBODY></TABLE>
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3 No two of the number's digits are equal --True
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<TD align=left width=316 height=20>4 None of the number's digits is greater than 4 -- False </TD></TR></TBODY></TABLE>
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5 The number has fewer than 6 digits --- True
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6 The product of the number's digits is not divisible by 6. i.e., 23569%6 = 3 ----- True
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7 The number is even. ---- False
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8 No two of the number's digits differ by 1--False
<TABLE cellSpacing=0 cols=1 rules=groups border=1 frame=void>
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<TD align=left width=316 height=20>9 At least one of the number's digits is equal to the sum of two other digits. (Any of the digits may be equal, as long as all 3 digits are distinct... for example: {2, 2, 4} or {2, 3, 5} ) </TD></TR></TBODY></TABLE> i.e., 2+3 = 5 & 3 + 6 = 9 ---- True
</TD></TR></TBODY></TABLE></TD></TR></TBODY></TABLE></TD></TR></TBODY></TABLE>
So all True Indexes are 23569
Which is a solution for this problem
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Posted by Pandu
on 2004-12-30 09:11:50 |
Best Solution
