unforum

[Reason]

[SOLVED] #019 - Red - Magic Numbers

[tanner]

nines

[appleTRON]

[SOLVE]

[Reason]

I didn't think there was any point either

[tanner]

but the magic is in the nines )

[Leeravitz]

Bloody Whipsmart

[Scott]

so that's three, then.

The original postcards said "Hello World"
The Whipsmart site said "HELLO", after you watch the grass grow
My calculator says "hello", with some cute numistry.

[spugmeistress]

Why?

sorry, but maths tricks like this always prompted me to figure out how they worked, equations n all that. but its been a while since my maths gcse and i'm not getting very far so if any mathmo's can prove how this works it'd be much appreciated :)

so far i've got that the difference plus the reverse difference must always equal 1089, and that im guessing the reason why you cant have the end digits of your number be less than two apart is because that would always create a difference below 100, which i guess people would assume it would become double digit and therefore the reverse difference would also be double digits and that wouldnt be enough to get to the 1089. maybe it would work if you included the leading 0, not sure yet.

its the reversing bit that im having trouble with cos i cant think of a mathematical way of expressing this (maybe im being totally thick here) but i originally tried expressing the original number you chose as 100a + 10b + c which then the reverse would be 100c + 10b + a, which would make the difference 99a-99c. how you get the reverse of that is the bit im stuck on :s

no particular relevance to the solve, just trying to satisfy my own curiosity (and nostalgia for actual academic school subjects that tend to make sense)

rach =)

[StarryNight]

Here's how I see it:

Given a 3 digit number ABC, the reverse is CBA.

Since we are told to "take the difference", this implies that the smaller number will be subtracted from the larger number. Thus, we can declare that "ABC" to represent the larger of the two numbers and thus A > C.

For the following, I've taken each digit and put it in ():

Step 1: Find the difference between the number and it's reverse.

(A)(B)(C)
- (C)(B)(A)
---------------
(A-1-C)(9)(10+C-A)

Note: Since A>C, we have to borrow a one

Step 2: Add the difference to it's reverse

(A-1-C)(9)(10+C-A)
+ (10+C+A)(9)(A-1-C)
---------------------------
(10)(8 )(9)

Step 3: Add 200

1089+200=1289

Step 4: Divide by 5000

1289/5000 = 0.2578

Step 5: Multiply by 3

0.2578 * 3 = 0.7734

Edit: had to put in spaces to keep smileys from appearing.

[spugmeistress]

cool. that looks like it makes sense, but not necessarily in a way that i can tell whats going on. so i'm going to confuse things into probably extraneous equations n stuff, because jeb helped me get my head round it by reminding me i needed to simplify my brackets.

sooo.. we have

your first chosen number ABC = 100a+10b+c
reversed =100c+10b+a
the difference then comes out as 99a-99c, which you can simplify to 99(a-c)

now, the clause in the puzzle says it only works if a-c > +-2, but thats a lie, because it does work with 1 as well, you just have to remember to include the leading zero you get as a result so you are always working with a three digit number.

so, (a-c) can be any single digit number (i guess it could be positive or negative too but not sure how to check) from 1-8(possibly 9?) which makes your difference (99(a-c)) a multiple of 99. The 99x table, due to the wonder of the number 9, goes

1x99=099 990=10x99
2x99=198 891=9x99
3x99=297 792=8x99
4x99=396 693=7x99
5x99=495 594=6x99

the reverse of the number is always another number in the table, namely the multiple that adds to your original a-c to make 11. so, the reverse difference is 99(11-(a-c))
(havent worked out the why on the 11 thing yet, whether its just the magic of 9s or i can do an equation or something- in fact starrynights post probably makes sense of that bit for me)

difference + reverse difference has to equal 1089 to get the magic hello.

99(a-c) + 99(11-(a-c)) = 1089
99(a-c) + 99(11-a+c)=1089
99a-99c + 1089-99a+99c = 1089
1089=1089 woot!


so yeah, thats satisfied my curiosity, thought other people may be interested too :)

credit to jeb for IRC promptings and explanations :)

rach =)

[StarryNight]

[tanner]

its just the difference -- smaller from larger -- no matter WHICH is bigger

[JebJoya]

Yeah, I kind of realised that just as I was going to bed - the only way for it to be negative were if you were taking 174-471, which would have been immensely silly the reason for the gap of 2 is that you could get this situation:
302 - 203 = 99 (which is not 3 digits)

I think that covers everything that can be covered

Jeb

[Reason]

Just noticed a Jack of clubs on the lower left of this card. Its pretty well hidden...

[Seej]

What are those shaded bits top and bottom right? They look like they extend onto other cards.