- It is a four-digit number.
- Its largest place value is its one place.
- The squares of each of its digits are less than nine.
- Its thousandths didgit divided by its ones digits is 50%.
- The sum of two pf its digits is 0.
- The difference between its ones digits and its thousands digit is 1.
- The sum of all of its digits is 3.
- It has only one prime digit.
- It is greater than 2.
- Its tenths digit is 0.
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Pragabhava
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Malia
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1What have you done? Were are you stuck? – Pragabhava Nov 12 '12 at 17:57
1 Answers
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Item 4 is stated incorrectly: the quotient of two digits can be $\frac12$, but it can’t be $50$%.
The first two items tell us that the number has the form $a.bcd$, and the third tells us that $a,b,c,d\in\{0,1,2\}$. Item 4 says that $a=2d$. Item 5 says that two of the digits are $0$. Item 6 says that $|a-d|=1$; since $a=2d$, we must have $a=2$ and $d=1$, so the number is $2.001$. The remaining conditions are superfluous.
Brian M. Scott
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Small point: I'm reading that rule 3 says $a$, $b$, $c$, and $d$ cannot be $3$ because $3^2\nless 9$. Also, I've long read "fifty percent" to be like "fifty miles per hour" as in miles/hours or in the case of "50%" I read $50/100$ (literally per cent) and therefore 50% could be seen as an alternate way to denote $1/2$. – Todd Wilcox Nov 12 '12 at 18:05
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@Todd: You’re right about Item 3; I read too quickly and registered it as $\le 9$. I don’t consider $50$% an acceptable substitute for $\frac12$ in this context: the result of dividing one integer by another is not a percentage unless the context calls for one. – Brian M. Scott Nov 12 '12 at 18:13