correct formula

oranghijau · 2016-05-03 00:53:31

hye all,
can somebody help me to solve this question??

If
12345678=148
23456789=180
34567890=162

what are the correct formula to answer this question..
one formula can answer all this 3 question...TQ

Relentless · 2016-05-03 12:17:36

This is darn hard to do by trial and error, but I did come up with one artificial-looking system.

Add all of the digits together, multiply by four, and then add the last digit minus the fourth digit.

In other words, multiply the fourth digit by 3, the last digit by 5, all the others by 4, and sum to get the answer.

Last edited by Relentless (2016-05-03 12:34:09)

Relentless · 2016-05-03 13:02:46

Looking at it more algebraically, and dealing with only the method of multiplying each digit by a separate number and summing the products, I determined, using the notation

to denote the number multiplied by the nth digit, that only the set of numbers satisfying the following three conditions will evaluate to the correct answers:
1.
2.
3.

Last edited by Relentless (2016-05-03 13:03:31)

thickhead · 2016-05-03 15:42:06

What is going on here?Can any sane person explain to me?

Relentless · 2016-05-03 16:05:05

Hi thickhead, hahahah

What OP is looking for is not necessarily a mathematical formula, but any algorithm for manipulating those numbers into those answers. For example, the first line might be

, which works for only the first line because for example . The only rule is that exactly the same algorithm has to work for all three lines.

Last edited by Relentless (2016-05-03 16:15:58)

thickhead · 2016-05-03 16:21:25

Relentless · 2016-05-03 16:44:45

Why not?

Relentless · 2016-05-03 17:24:57

thickhead · 2016-05-03 18:53:01

Relentless,
Are you sure no - and / are involved?

oranghijau · 2016-05-03 23:00:55

Still didnt get the correct formula..
It says 1 formula can solve 3 question...
I got another 2 days to submit..;(

Relentless · 2016-05-04 05:17:41

Last edited by Relentless (2016-05-04 05:21:13)

phrontister · 2016-05-04 11:22:40

Hi guys;

I have a solution based on parts of posts #2 and #8, but it involves what I'd say is trickery.

Last edited by phrontister (2016-05-04 17:42:46)

oranghijau · 2016-05-04 22:53:18

Dear phrontister..
Answer for number 3 is 210 if using that formula..

Relentless · 2016-05-04 23:30:42

Hi phrontister (:

Ignore the OP, Your formula:

Satisfies the three conditions of post #3 and is also correct.

I meant to add that it is expected to be solved without repetition of numbers as well.

But regarding the supposed solution with extra conditions - Use the numbers once in their given order to produce the answers using only +, * and () in the same manner - while it might exist and be valid, I would not trouble myself very much over it, since the creator of this problem on a different site seems too mathematically illiterate to understand what we are even doing here.

Last edited by Relentless (2016-05-04 23:42:26)

phrontister · 2016-05-05 01:11:31

Hi oranghijau;

Answer for number 3 is 210 if using that formula..

210 is incorrect, so I suppose you made an input error.

There are a number of easy ways to check the answers of the sums in my post that avoid input errors. Just copy the whole line before the "=" sign and paste it into a software or online calculator on your computer that accepts such input. Many do.

eg, Mathsisfun: here, or WolframAlpha here.

You can even use the address bar in Google Chrome and Microsoft Edge...just don't press Enter, otherwise you'll get an error message because of the large input size.

You'll find that the answers I posted are correct.

Relentless · 2016-05-05 01:25:48

phrontister wrote:

You'll find that the answers I posted are correct.

I concur However, there are infinitely many correct solutions of a similar type.

Last edited by Relentless (2016-05-05 01:26:48)

oranghijau · 2016-05-05 01:36:08

if calculate one by one using normal calculator (not copy and paste)...it still get 210.
is there any other way?

phrontister · 2016-05-05 01:36:14

Hi Relentless;

Yes, I can see that.

Your previous post's formula works perfectly well.

I usually don't mind puzzles like this and have a reasonable success rate with them, but trying to find a solution can sometimes be as exasperating as determining the value of the next term in a series. You can either see it or not, and the greatest klutz can surprise.

I tend to call it a day after my brain has switched off and I've headbutted the keyboard...but then, after a good night's sleep, sometimes light dawns at dawn's light...or in the middle of the night.

I may try this puzzle once more, again.....or not.

phrontister · 2016-05-05 01:43:08

oranghijau wrote:

if calculate one by one using normal calculator (not copy and paste)...it still get 210.
is there any other way?

This one, which is the one in my post, yields 162: 3+4+5+6+7+8+9+0+3+4+5+6+7+8+9+0+3+4+5+6+7+8+9+0+3+4+5+6+7+8+9+0-3+4-5+6-7+8-9+0

This one yields 210: 3+4+5+6+7+8+9+0+3+4+5+6+7+8+9+0+3+4+5+6+7+8+9+0+3+4+5+6+7+8+9+0+3+4+5+6+7+8+9+0

Did you use all "+" signs, as in the second one, and overlook the four "-" signs that are in the first one?

oranghijau · 2016-05-05 02:09:28

plus all digits by 4 times (-D1 + D2 - D3+ D4 - D5 + D6 - D7 + D8)..
its like this??

oranghijau · 2016-05-05 02:30:44

i submit the formula and answers..its not correct..
they told me the numbers just can use one time only..

phrontister · 2016-05-05 02:54:36

oranghijau wrote:

plus all digits by 4 times (-D1 + D2 - D3+ D4 - D5 + D6 - D7 + D8)..
its like this??

That is very different from what I did, and gives a very wrong answer.

My method uses several sets, because, although they're not exactly spelt out to the letter, I understood the rules to be these:
(a) only full sets can be used in the calculation;
(b) the numbers must retain their original sequence;
(c) no out-of-sequence numbers can be used (even though that number may be one that appears in the set);
(d) no new numbers (ie, numbers not in the set) can be introduced.

In your format, my formula looks like this:

4(D1+D2+D3+D4+D5+D6+D7+D8)-(D1-D2+D3-D4+D5-D6+D7-D8)

The second set looks different from that in post #12 because of the effect of parentheses on the minus signs.

I use the set more than once - which is not allowed - and so Relentless's method in post #14, in which the set appears only once, suits better.

Last edited by phrontister (2016-05-05 03:18:51)

oranghijau · 2016-05-05 03:04:10

dear phrontister and all friends..

a good news..i'm the winner..
TQ for all helping friends..

very proud of you..

phrontister · 2016-05-05 03:09:11

Congratz!

But how did you manage to win with an incorrect formula?

oranghijau · 2016-05-05 03:21:59

that formula are almost near to the calculation..
but what the mos shocking me is..just using microsoft excel..

the simplest formula..R35

1 x 3 = 3 2x3=6 3x3=9
2 x 5 = 10 3x5=15 4x5=20
3 x 3 = 9 4x3=12 5x3=15
4 x 5 = 20 5x5=25 6x5=30
5 x 3 = 15 6x3=18 7x3=21
6 x 5 = 30 7x5=35 8x5=40
7 x 3 = 21 8x3=24 9x3=27
8 x 5 = 40 9x5=45 0x5=0
=148 =180 =162

Math Is Fun Forum

#1 2016-05-03 00:53:31

correct formula

#2 2016-05-03 12:17:36

Re: correct formula

#3 2016-05-03 13:02:46

Re: correct formula

#4 2016-05-03 15:42:06

Re: correct formula

#5 2016-05-03 16:05:05

Re: correct formula

#6 2016-05-03 16:21:25

Re: correct formula

#7 2016-05-03 16:44:45

Re: correct formula

#8 2016-05-03 17:24:57

Re: correct formula

#9 2016-05-03 18:53:01

Re: correct formula

#10 2016-05-03 23:00:55

Re: correct formula

#11 2016-05-04 05:17:41

Re: correct formula

#12 2016-05-04 11:22:40

Re: correct formula

#13 2016-05-04 22:53:18

Re: correct formula

#14 2016-05-04 23:30:42

Re: correct formula

#15 2016-05-05 01:11:31

Re: correct formula

#16 2016-05-05 01:25:48

Re: correct formula

#17 2016-05-05 01:36:08

Re: correct formula

#18 2016-05-05 01:36:14

Re: correct formula

#19 2016-05-05 01:43:08

Re: correct formula

#20 2016-05-05 02:09:28

Re: correct formula

#21 2016-05-05 02:30:44

Re: correct formula

#22 2016-05-05 02:54:36

Re: correct formula

#23 2016-05-05 03:04:10

Re: correct formula

#24 2016-05-05 03:09:11

Re: correct formula

#25 2016-05-05 03:21:59

Re: correct formula

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