A little maths problem I posted on my blog became one of my most popular posts, and still draws traffic daily from Google.
Here’s something for you guys to try out at home – don’t worry, there’s nothing difficult, only adding and subtracting, but make sure the difference between the 1st and 3rd digits is at least 2 in your number.
Do let me know the number you chose and the answer you got.
Don Charisma 
I just remembered why I am a writer. 🙂
😉
if 2+5=16 and 6+8=7, what is 6+2? solve bro
Presumably, “+” here means some binary operator other than addition. There are infinitely many binary operators that satisfy the two equations, giving infinitely many solutions. One of those binary operations is the sum of a multiple of two unknowns. We can therefore find one possible answer to the silly question by solving:
If 2x+5y=16 and 6+8=7, what is 6x+2y.
Working:
2x + 5y = 16
6x + 8y = 7
6x + 15y = 48
7y = 41
y = 41/7 = 82/14
2x + 205/7 = 16
2x = 16 – 205/7
x = 8 – 205/14 = (8 * 14 – 205) / 14 = (112 – 205)/14 = -93/14
6x = -558 / 14
2y = 164 / 14
6x + 2y = -394 / 14 = -198 / 7
This gives the unwieldy answer -198/7.
This is probably not the answer Chris hoped for. He ought, therefore, to ask his questions more carefully.
The number first thought of is 100a + 10b + c, for some (a,b,c) where {a,b,c} is a subset of {0,1,2,3,4,5,6,7,8,9}. It’s reverse is 100c + 10b + a. The difference is 99 x |(a – c)|.
The difference is therefore 99n, where n is a member of of {2, 3, 4, 5, 6, 7, 8, 9,}.
In H~T~U notation (hundreds, tens and units), 99n is (n-1)~9~(10-n) for all eight possible values of n, and its reverse is (10-n)~9~(n-1), which also happens to equal 99 x (11-n). For example, if n is 3, then 99n is 297,and its reverse is 99 x 8, which is 792.
(n-1)~9~(10-n) + (10-n)~9~(n-1) = 900 + 180 + 9 = 1,089 Q.E.D.
Very nice, hope all our readers got that.
And as you have shown, the answer will ALWAYS be 1089, so long as you follow the rules. Good trick for your friends though.
Numbers give me a headache Don.
Don’t worry, I won’t put anymore on here…
My son would love this ~ he is a Maths tutor for A level students in Madrid.
It’s good to show students, even at that level, how simple steps produce unexpected results in maths.
Reblogged this on and commented:
One of my ex-boyfriends a loong time ago was quite a math wizard. My math knowledge is at the 3rd grade level which is why I should probably start relearning with my daughter who is 9. I’ll save this here for any of you who get a kick out of it (and for myself for future study!).
Thanks for the reblog – it’s never to late to learn. People tend to put down their maths skills, and a recent report in the UK suggested that parents often put their children off maths by saying how bad they are at it.
Thanks for the reply. Let’s see how long I can fool my kids. 🙂
My 10 year old liked this one. If it gets them interested in maths then it’s worth posting it.
Yes, any number chose will result in 1089. But, step 3 is wrong, if you take the large number from the small number (using your example) you end up wit -297, not 297, in which case the rest of the math doesn’t work out. Seen this before, still fun.
Didn’t even spot that. Duly fixed. Thanks.
Part of my CDO, it’s like OCD, but with the letters in their proper order.
🙂
I see a trend here……
669
966
966-669=297 ditto
699
996
996-699=297 ditto
Pretty cool eh?
I’m going to skip this one Don. Just finished doing our taxes and I’m all mathed out.
Leslie
To be expected – I finished mine in January and have only just recovered.
I chose 497…and my final answer is 1089…weird that i had 297 and 792 also…creepy
Creepy indeed
Reblogged this on BookwormFavorites and commented:
My Example is:
832
238
832-238=594
495
594+495=answer
I totally got it! Amazing how powerful and fun math can be if you try!
Your Bookworm
Thanks for the reblog. Yes, it’s one of those amazing things with maths that sort of appears from nowhere.
Reblogged this on Human Relationships.
Thanks for the reblog. Do let me know what number you picked.
🙂
Reblogged this on Blogger at the Edge of the Universe. and commented:
Cool! 🙂
Thanks for the reblog. Do let me know what number you picked.
965.
Neat trick, by the way. The answer’s always the same no matter what number is used (as long as it follows the rules).
🙂
Indeed well done.
I like those kinds of things.
The question is – why is it always the same answer?
First: any three-digit number where the 1st and 3rd digits are 1 apart gives 99 upon subtraction of its opposite. Any three digit number whose 1st = 3rd obviously gives 0.
Second: every other three-digit number when subtracted by its opposite always gives a three-digit number that has a 9 as its second digit, whereas its 1st and 3rd digits will always add to give 9. When adding, then, its essentially like adding 999 by 999.
Aaaaaaaaaaaaaaannnnnnnnnndddd there you go!
Very good, I’ll have to put up more challenges for you!
cool tips to show off 😉
tnx
Do let me know what you chose and what your final answer was.
954 = 1089
982 = 1089
387 = 1089
the first number can’t be 459 but 954 it’s ok
459 works just fine for me.
954-459 = 495 + 594 = 1089
but 459-954 = – 495 + 594 = 99
Thanks, I made a small error in the original which has been fixed – you must take the small number from the larger number, so it will be 954 – 459 all the time.
Apologies – I need someone to proof read before posting this stuff.
ok now i got it 😉
My mistake!