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Stumped by 4th grade math!!!

So a friend of mine was helping her 4th grade neice with her math homework, and butted heads with this problem, in which you are to solve for each letter, with each letter being a unique integer:

HOCUS
+POCUS
--------------
PRESTO

Three fairly intelligent adults have now all knocked our heads against this and we can't come up with a viable solution. Here are our assumptions, maybe you can tell us where we're going wrong, but it looks unsolvable:

P = 1. It's clearly carried over from H+P in the previous column, and it couldn't be anything higher than 1.

If P = 1 then H has to be 9 or 8 for H+P> 10 (if it's 8, then there has to be carryover from the previous column, O+O=E)

R has to be 0; if P=1 and H = 9 or 8, then H+P (or H+P+1, carryover from the previous column) has to be 10; it could be 11 (if H is 9 AND there's carryover from the previous column) but that would make R 1 and P is already 1; so it could only be 0)

O has to be even since O=2S and there can't be any carryover from a previous column.

We've tried brute force and couldn't find any workable solution in which each of the letters represent a unique number. HELP!

You can use the solver at http://www.tkcs-collins.com/truman/a...alphamet.shtml to find the answer, which may or may not aid you in the process of actually coming up with the solution.

wow, that's a neat tool elsesomebody. who has that kind of time on their hands??

This is a puzzle, not math -ican't believe a 4th grader could get this

HOCUS
+POCUS
--------
PRESTO

It's easy to understand thatthe H and the P couldn't be a 0 because a number wouldn't start with 0 -- andthat numbers shouldn't repeat... but damn --

There's gotta be something obvious that I'm just missing... (I'm goiing to return my BS in Math cause clearly I've gotten too stupid)

the answer came from the site

92836 C=8 E=5 H=9 O=2 P=1 R=0 S=6 T=7 U=3
+12836
------
105672

And we wonder why "Johnny" can't add. :rolleyes: What does this have to do with math?
This frustrates me...and I'm 42 years old. Granted...my math skills suck, and always have, but I don't see how a 9 year old is supposed to get this. Where's Dan Brown when you need him? :D

I remember getting extra credit problems like that...but nothing that was actual graded work...

I'm glad ya'll have the patience for it. . . I just looked at it and went "pffft. . . that's just gonna piss me off" and moved on :)

I agree with the logic that you posted.

So working with P,R=1,0, there can be no carryover to the fifth colum, to be less then 5 because the sum must be less then ten and already we know that it must be even.

So O is either 2 or 4, making S equal to 1,6, or 7. 1 is already taken, so it must be six or seven and then T must be odd, from 12 or 14.

With T being odd, we know it isn't 1 or 3, and 9 is taken. So T = 5 or 7. T can only be 5 if U = 2.

Now 1,2/4, 5/7, 6/7 and 9 are taken.

So I tried O=2, implying E= 4 or 5, and S= 6. Since we are assuming O=2, U can't be 2, so T = 7. Accordingly, U= 3 Also, since T=7, S is going to be even (no carried one)

So 1,2,3,(4or5),6,7, and 9 are taken. So C must be the an even number, C=4or8. If C=4, then S=8. But S is already 6, and (8+8)= 16. Further, if C was 4, then since O is 2, E would be 4, and C can't = E.

Now you plug it in to double check.
H=9, O=2, C=8, U=3, S=6,
P=1, O=2, C=8, U=3, S=6,
P=1 R=0, E=5, S=6, T=7, O=2.

And it works.

This took my about 15 minutes. I'm an adult university student; a programming course I took didn't directly give me credit for a programming course I need, so I'm currently in a 1 credit, 1 hour a week, 'Logic 273' course. This is simple now, but is almost exactly like the questions we started with in January. There are brillaint people in class that come up with elegant solutions. I'm more of a brute force or methodical worker myself. Must be a pretty hardcore grade 4 teacher.

I guess it took me more then 15 minutes. Mal hadn't posted the solution yet when I started. I had to use paper and I was eating lunch at the time, so I didn't rush back. I should have refreshed.

I started on it, then decided to Google. I came across this page from some book. I'll quote the relavant portion of it:

Quote:

Our examination of concrete judgments of fact revealed that the fulfilling conditions for a judgment are often given in presentations rather than in previous judgments. Further, they revealed that the link between the conditioned and the fulfilling conditions can be given in cognitional structure itself. Experience, understanding and judgment work together, as we have indicated briefly already. Understanding mediates between the levels of experiencing and judging. How do we know that our understanding is correct? How do we know that our definitions of color are correct? The purpose of this present section is to explore these questions.

Our appeal, again, is not to some theory of knowledge but to our own experience of knowing. If you have tried to do the addition sum suggested in the preliminary exercises, hocus, pocus, presto, you will have been involved in a series of individual insights. Some of them will be correct; you think a little and realize that they must be correct and, secure in that knowledge, you move on to the next step. For instance, it is not difficult to see that P must be equal to one. There are no single numbers which, when added together along with one, will give you twenty. So that the P of presto must be equal to one. All other possible values are excluded. No further questions arise. There is no need to delay over the matter; you move on to the next clue. Write down everything you know about the values of the letters. Substitute the values that you know. Look for clues. Is there any other letter that we can pin down? You can say that the letter O is even; any number added to itself gives an even number. What about R? It must be either 1 or 0. But it can't be 1 because P is already 1. So it must be 0.

You might then focus on H and say it must be 9. But must it? Consider other possibilities. Ask further questions. Oh, yes, it could be 8, if there is a carry one from the previous column. After that it is a matter of trial and error. The important thing is to recognize the point at which you know that you are right and must be right, and the point where you are still considering possibilities and still asking questions. In mathematical examples it is very clear when we have reached a correct insight because there is a checking process that shows that it is correct and a complete closing off of further questions indicating that nothing further could interfere with the conclusion already reached. A mistaken insight is open to be overturned by the asking of further questions and the realization that we left out some possibility or necessity.

Note then that insights give rise to further questions. There may be questions about the matter in hand which have not been settled and other possibilities have to considered and checked. Or our questioning may conclude that the matter in hand has been solved and further questioning on that matter is fruitless, so we spontaneously move on to further matters which have yet to be understood.

Hence we introduce an operational distinction between vulnerable and invulnerable insights. We operate spontaneously on the principle that an insight is invulnerable if no further pertinent questions arise that could overthrow it. Contrariwise, an insight is vulnerable if there are further pertinent questions to be asked and answered about the matter in hand. This is a law immanent and operative in cognitional process. Go over your experience of solving any of the puzzles and you will notice it at work. You know that a student in class has solved a puzzle, when you see him relaxed, gazing about the room, getting bored as he waits for the others to find the solution. He has no further questions to ask and it is boring to spend more time on the matter.

This criterion has to be treated with some care. It is not as easy as it sounds. An insight is invulnerable if no further pertinent questions arise, but we have to allow the questions to arise. We have to be open to all possibilities, we have to be able to ask the relevant questions, we have to have the time and the interest to follow up the further questions, we have to be able to exclude other distractions as we pursue our investigation to the end. Questions can come to an end for many reasons other than that we have reached an invulnerable insight. So we have to lay down further qualifications.

Give further questions a chance to arise. The first insight, however brilliant and exciting, may not be correct. You have to ask the question for reflection, is it true? is it correct? and that may reveal that something has been left out and the whole process has to start again. A judgment is a rash judgment if it is made hastily with too little reflection and no time for further questions to arise.

We try to prevent further questions arising if we are unwilling to change our established position and feel that asking further questions may undermine our position. So we avoid the further question by reinforcing our limited stance, digging in our heels; we resort to rhetoric and prevent reflection. Openness to all further questions is a characteristic of the pure desire to know and is the knife that cuts through prejudice, bias and dogmatism. We can avoid all mental activity by indulging in a well-meaning activism which aims at changing the world without first understanding it.

We noted before that each individual judgment is dependent on a context of other judgments. Our present judgments are dependent on our past judgments. Our judgments are linked to our direct insights and our various experiences. There is a whole context of our education, mental habits, ways of thinking, opinions, and judgments that has been built and intertwined over a lifetime. There can seem to be a vicious circle here. Single judgments depend for their validity on a context of prior judgments. But if the prior judgments are wrong or warped or biased, how do we get out of the mess? This is something like the problem of the hermeneutical circle. To understand the whole of a book you have to first understand the parts; but you cannot understand the parts without understanding the whole. This seems to lead to a logically impossible position.

We would solve this by appealing to the self-correcting process of learning. How, in fact, does our understanding develop? It develops in small painful increments. We get a vague idea of the whole from the table of contents and we get a vague idea of the part by skimming the first chapter. We go back to the whole and have a better understanding as we return to the parts. It is the process of learning that breaks the supposed vicious circle.

It is the same with a context of judgments that has gone a little bit awry. We do not have to reject the whole lot in order to start again afresh. Descartes recommended the system of methodic doubt; discard everything that can be doubted and, if there is anything left, start there. This seems rather radical especially as, if you start doubting everything, there is no obvious place to stop. But Newman suggested an alternative procedure; accept in general what you reasonably can, but if you spot a mistake dig it out root and branch. He was recommending the self-correcting process of knowing. Keep asking questions, be open to alternatives. If there is an incoherence it will eventually be exposed. If there is a mistake, then, it will show up by not fitting in with other data. We can learn from our mistakes. Why did we overlook such data, what other mistakes might have been made; correct the context and see how that effects other things. The context that is skewed can be straightened out, reoriented, and purified.

The process of reflection tends to be discursive not deductive. It is discursive in the sense that we proceed step by painful step; we often take two steps forward and one backward. Questions in one area tend to a limit where we are satisfied that we have sufficient evidence; maybe in another area we turn up evidence that would have a bearing on the previous material. We go round in circles, we move up spirals, we go over our tracks, we make mistakes but the later context will often reveal them to be mistakes. Our thinking is rarely deductive; we rarely proceed logically from premises to conclusions. That may be the form in which we present our conclusions but that is not how the whole process of questioning, imagining, formulating, defining, reflecting, evaluating, etc. goes on. Our minds conduct a kind of mixed up conversation with ourselves in which there are many voices, many levels, many desires operative, but the general orientation is towards the reflective understanding leading to judgment.

Interference with the process of knowing usually comes from the motive force, from the temperament, the intention, the self-interest of the knower. Rashness and indecision are usually rooted in temperament. Some people are prone to jump at the first possibility; they have not the patience to wait, to think, to reflect. Others have sufficient evidence but are paralyzed by fear of being wrong. They are so afraid of making a mistake that they do nothing and affirm nothing. The ditherer cannot make up his mind.

More serious distortions can be introduced by twisted motivation. To live continuously by the pure desire to know and to be open to all questions is a rare achievement. More common is taking up a position that one likes and then finding the evidence to bolster it.

If you can follow that without your eyes crossing...

Quote:

Originally Posted by Bill O'Rights

And we wonder why "Johnny" can't add. :rolleyes: What does this have to do with math?

This is a great primer for teaching a student how a mathematician actually tends to think when solving a problem---without scaring the student away with explicit algebra. It's great for gifted students. But...grade 4? Poor kid.

I vaguely remember having a problem similar to this in 4th or 5th grade, and being just as stumped, aggravated, and feeling stupid, with my dad just as much so because he couldn't figure the damn thing out either.

4th grade math my ass. Maybe 6th, but 4th? You gotta be kidding.

I remember reading a book when I was a kid about a "Wayside school" or something, where the school was supposed to be really long but the builder screwed up and held the blueprints sideways so he built it really tall instead. Anyway that book had a whole bunch of math problems like that and a bunch of other logic problems with True False tests etc. Anyone else remember that book (or am I just crazy)?

Ninja Edit: Score!

i am going to agree with some other people... really what does this have to do with math... i understand the need to depart from normal math to stimulate intrest but how to repitions of things like this really help the student?

Quote:

Originally Posted by lurkette

So a friend of mine was helping her 4th grade neice with her math homework, and butted heads with this problem

Did she hand in her results (or lack of results) yet? I'm interested to know what the teacher had to say about the problem.

I've done calculus thats easier then that shit lol.

If I spent long enough it would be sorta easy or had one of the numbers, but wtf?

Who the hell in their lifetime is gonna have to figure out that the secret numbers HOCUS + POCUS = PRESTO lol?

Then again that applys to about half of math you learn :)

In 4th grade they were teaching us our times tables... I wasn't even awake enough to read through and understand the first post's question :lol:

After seeing it here last week, I showed it to my 3rd and 4th grade sons and we/they had fun talking about it and thinking about how to solve it, but they did not figure it out. I bet when I get home from work today, my 3rd grader will have showed some of his friends and will tell me about what they did/thought ...then go outside and shoot some hoops in the driveway :)

In any case, I think that teaching critical thinking processes for how to attack a problem is very important no matter what you end up doing in life ...but maybe that's why I'm a BSME engineer. If you can't think that way, you can always flip burgers, or now adays, work the register since you don't even have to know how to add or subtract to do that anymore.

I don't even know how to go about that problem without using Algebra...

What kind of 4th grader is taking Algebra?!?! That was an "Advanced" course for me in 8th grade. Of course I was schooled in Ga, so maybe we really are that far behind...

If you don't have kids this age, how would you know?

Both my 3rd and 4th grade kids going to the normal local public school in suburan Philadelphia, are now learning algebra. Basics, like the concept of variables and how to find out what value they actually might be. Simple stuff to start but it went on from here to more interesting concepts; initially stuff like if A = 1, B = 2, C = 3, D = 4 ....etc. How many ways can you make a "math sentence" that equals 5? ...so A + D and B + C, etc. I bet some of us adults can even do this ;)

Red -

That was some explanation! ;)

Lurkette, you suck. It took me over an hour to get this. I could have been watching paint dry ;)

hocus
92836
pocus
+12836
--------
presto
105672

There goes an hour of my work day - I think this is not an overly complicated problem. The best method of trying to solve it is to start with the beginnings as shown by miriad people above and work out what each letter is not.
Given that p=1, and can't be anything else, r has to be 0, which makes h =9.
From this start, you can deduce that none of OCUS are 5 (as the resulting bottom line would be either 0 or 1, then O needs to be even, but not 6 or 8, because it invalidates "R=0"
and so on.

From here I did a bit of If this, then that, until I got an invalid result.

Quote:

Originally Posted by spindles

h does not have to be 9, it could be 8 due to carryover from the previous column. You know that r is equal to 0 because you can't have a situation where there is a carryover and h is 9, because r cannot be 1. So if h can be 8 or 9, then none of the OCUS letters can be 9, because the result of two of these letters would result in 18 without the carryover and 19 with, but none of these answers would be possible because either you would use up both 8 and 9, which are the only possible values for h, or you would get 9 for two different letters. Also, as spindles mentioned none of the OCUS letters can be 5. It think there was some other deduction that I made, but I can't recall now.

The funniest thing about this is that I doubt if their teacher would be able to solve that problem himself/herself without seeing it in a book first lol

Quote:

Originally Posted by bookie05

The funniest thing about this is that I doubt if their teacher would be able to solve that problem himself/herself without seeing it in a book first lol

:lol: Probably right!

I could probably have done it faster back then than I could do it now... I liked that secret code type stuff. Though now I think it's useless crap. It seemed to me that the years 1-6 of math has so much non-math in it that it could be reduced down to two years, then have them do three years of algebra and a year of geometry to finish up elementry school. Then start them in Jr High with Trig, Precalc, and then start Calculus in grade 9. Separate out the other stuff into a critical thinking subject that teaches them how to think to solve stuff like that and how to integrate everything into real world thinking and problems.

And as a side note, that's just my opinion, and I'm not saying that it's the correct way things should be done.

Quote:

Originally Posted by ForgottenKnight

And as a side note, that's just my opinion, and I'm not saying that it's the correct way things should be done.

It's a hell of a lot better than the mindless regurgitation of textbooks schools "teach" now.

Quote:

Originally Posted by madcow

I loved those books.. they were silly yet entertaining. I think I still have them somewhere /slightly embarassed

ok so I really really suck at math so I didn't really give it a good go. I spent maybe 15 seconds on it. Hell I did the a=1 b=2 and so on even though lurkette said that wasn't how it was done.

I know the last post was a month ago but I think I have the answer
hocus
+pocus
--------
presto
or anything else you want it to be

have we already forgotten Merlin.............. hocus pocus........ITS MAGIC :thumbsup:

Sometimes its good to give questions they can't answer. It shows them where lifes bar really is now and then.

As a rule we are way to easy on kids, and it shows when people come to me for a job.

I am new here. I was searching for this answer as my year 8 child has entry exam full of these problems,JUST to get into year 9 .The school said they wanted to Separate the wheat from the chaff. I am in Australia, so don't know what level that would equal where you are.

no doubt anyone who couldn't solve this problem was criticized for it. I remember having detention for not being able to solve this kind of shit.

Quote:

Originally Posted by t3m3st

no doubt anyone who couldn't solve this problem was criticized for it. I remember having detention for not being able to solve this kind of shit.

Pardon if I find that a bit hard to believe. I used to feign stupidity in order to get out of doing work and I don't recall detention for it. Detention for other things sure but not math.

Quote:

Originally Posted by tscrib

a year 8 student here, would probably be about 12 years old... year 9 would be the first year of high school which would make the kid 13ish...

a 4th grader would be about 8 or 9 ish...