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Melodi
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Oct-29-01, 10:24 PM (EST) |
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"Addition math problem!"
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Below are some numbers and they have to equal 159 you can add or subtract -- that's it.....you can group the numbers together (like 521-306) but you can't take them out of their order.
5 2 1 3 0 6 8 4 = 159
A friend emailed me with this, we are trying to help her daughter with her homework and so far 5 adults can't figure it out, pretty sad. |
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alexb
Charter Member
672 posts |
Oct-29-01, 11:43 PM (EST) |
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1. "RE: Addition math problem!"
In response to message #0
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LAST EDITED ON Oct-29-01 AT 11:46 PM (EST)
>Below are some numbers and they have to equal 159 you
>can add or subtract -- that's it.....you can group the
>numbers together (like 521-306) but you can't take them out
>of their order.
>
>
>5 2 1 3 0 6 8 4 = 159
>52 - 1 + 30 - 6 + 84 = 159 Do you think providing an answer to such a problem will help the girl learn anything? A better way would be to advice her parents - your friends - to confront the teacher who gave such an assignment with the question, what are the students supposed to learn from this exercise? The only way I could think of how to approach the problem was via digital roots. I digital root of a number is its remainder of division by 9. The most important property of digital roots that they can be computed by adding the digits of the number. For example, 521 = 8 (mod 9), which means that 8 is the remainder of division of 521 by 9. But also, 8 = 5 + 2 + 1. How do the digital roots help in solving your problem? The digital root on the right is 6: 159 = 6 (mod 9). Any sign distribution on the left that solves the problem must result in the same digital root. But working with digital roots is easier than working with 2 or 3 digit numbers. If all digits on the left are taken with the sign plus, like 521 + 31 + 684, the result will have a digital root of 2, because 2 is the sum of all the digits on the left modulo 9. What digits could be taken with the sign minus so that the digital root on the left would become 6? |
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briant
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Nov-01-01, 06:40 AM (EST) |
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3. "RE: Addition math problem!"
In response to message #1
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>The digital root on the right is 6: 159 = 6 (mod
>9). Any sign distribution on the left that solves the
>problem must result in the same digital root. But working
>with digital roots is easier than working with 2 or 3 digit
>numbers.
>
>If all digits on the left are taken with the sign plus, like
>521 + 31 + 684, the result will have a digital
>root of 2, because 2 is the sum of all the digits on the
>left modulo 9. What digits could be taken with the sign
>minus so that the digital root on the left would become 6? Interesting approach, but I am left wondering what the process would be to determine how to create a digital root of 6 other than by trial and error...
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alexb
Charter Member
672 posts |
Nov-02-01, 07:03 AM (EST) |
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4. "RE: Addition math problem!"
In response to message #3
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LAST EDITED ON Nov-02-01 AT 07:05 AM (EST)
>Interesting approach, but I am left wondering what the
>process would be to determine how to create a digital root
>of 6 other than by trial and error... There is no reason to create the digital root of 6. It's 6. So I interpret your question as asking Is there any considerations beyond working with digital roots that lead to the answer more directly than random sign selection? Yes and no, although some trial and error involved, if you try working out the problem you'll see that some variants are immeditaely unsuitable. Replacing the sign of a number from plus to minus means subtracting the number twice. The sum of all digits is 2. Obviously, if you take 5 with the sum minus, the resulting digital root will be 1: 2 - 2·5 = 1(mod 9). Think along these lines. Working with digital roots makes arithmetic easier, but does not reduce the problem to, say, a status of a theorem where one would know up front what to prove. Some search is required.
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Kevin Cline
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Nov-07-01, 09:27 PM (EST) |
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5. "RE: Addition math problem!"
In response to message #1
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You can constrain the possible solutions using digital roots,
but it's faster to come up with approximate solutions and then
adjust them to get the answer required:5 2 1 3 0 6 8 4 52 + 13 + 0 + 6 + 84 = 155 too small by 4, let's make it bigger 52 + 1 + 30 + 6 + 84 = 173 too large by 14 now it's obvious to change +6 to -6 and +1 to -1 52 - 1 + 30 - 6 + 84 = 159 |
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alexb
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Nov-28-01, 09:42 PM (EST) |
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10. "RE: Addition math problem!"
In response to message #8
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I think a child must be of a certain mindframe. There are too many possible arrangements for a teacher to be sure that a child will solve the problem successfully. An average child will surely get some practice but is unlikely to solve the problem. Besides getting frustrated, the child may form an opinion that mathematics necessitates silly computations with no goal in sight. Practice should not be disguised as an open ended problem. Children must be aware of what they are doing and why. On these grounds I think the problem at hand is not a good homework assignment. |
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mike b
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Nov-28-01, 09:42 PM (EST) |
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9. "RE: Addition math problem!"
In response to message #0
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>Below are some numbers and they have to equal 159 you
>can add or subtract -- that's it.....you can group the
>numbers together (like 521-306) but you can't take them out
>of their order.
>
>
>5 2 1 3 0 6 8 4 = 159
>
>A friend emailed me with this, we are trying to help her
>daughter with her homework and so far 5 adults can't figure
>it out, pretty sad. Try 52-1+30-6+84=159 |
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