Math Is Fun Forum

That's the formula in post #14 by Relentless.

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.

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.

Hi guys;

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

Definitely a team effort!

I'd still be poking away at it in the dark if it wasn't for the insight of the other team members.

Raining outside...can't dig holes in the mud!

This is the best I've got so far:

X = 4.

Hi Anna;

You should compare columns with columns and rows with rows, not columns with rows. The 'x' diagonal only goes in one direction (NW to SE), which throws the expected balance out, but there is another way of looking at this that shows we have the balance we need.

Here are two coloured images from my spreadsheet to help demonstrate. All green cells contain "2" and all blue cells "3".

In this version, if you draw a line through the centre to two cells opposite to, and equidistant from, each other, you'll find that one of them will contain a "2" and the other a "3". Always. In the following examples of this, the first letter denotes the row and the second the column.

Ae ("2") is opposite fB ("3").
OR ("3") is opposite RO ("2")

And so forth, and so fifth...etc.

There are an equal number of each colour/number, distributed equally in a balanced pattern about the 'x' diagonal.

This version comprises two diagonally-cut halves (with the NE sector rotated 180°) alongside each other for comparison. You'll see that all "2"s and "3"s in the right-way-up image align exactly with their respective "3"s and "2"s counterparts in the 180°-rotated image. That pattern applies throughout, which could not happen without 100% balance.

Brimming with balance!

Just had a thought and checked my images. There's a critical error! Grumble! Back to the drawing board!! Maybe you're right. Have to go out now for a few hours, and will look at this again this evening.

Ah...yes! Exactly, thickhead.

X = 3.

And thanks for spotting the flaws in my table.

I've got the following for those:
e = 2 + 30*3 = 92;
f = 31*3 = 93

Because f is the 31st term from A, and A = 62, then f = 62 + 31 = 93...and e is 1 less.

Hi Relentless;

Both correct!

My HP 32SII (below), working 'perfectly well' again! I must've walked off with it, and the refund! I'll have to 'pay' the shop a visit...

Yes, that is $1 less than $100...which is the initial amount of Mum and Dad's loan.

However, the above quote should read: Now you owe your mum $49 and your Dad $49 so 49+49=98 less the $1 with u is $97...which is the cost of the shirt.

Adding, instead of subtracting, the $1 only seems to be going in the right direction with it because of the close proximity of $99 to $100. If the $100 were some other figure - like $1,000,000 - it would be obvious that something was up, even though one figure is just as (ir)relevant as the other. 

The correct sum for arriving at $100 is this:
$49 + $49 + the $2 already returned to Mum and Dad = $100...which is the initial amount of Mum and Dad's loan.

Here's the same chart in 'code' tags.

If you want to align the single-digit numbers with the right digit of the double-digit numbers, you'd have to include spaces where needed...but this is the simple solution.

Ok, thanks. I think I have the picture now.