wu :: forums « wu :: forums - (71-1)(71+1) = 71 » Welcome, Guest. Please Login or Register. Sep 23rd, 2018, 7:16am RIDDLES SITE WRITE MATH! Home Help Search Members Login Register
 wu :: forums    riddles    medium (Moderators: ThudnBlunder, towr, Icarus, Grimbal, SMQ, Eigenray, william wu)    (71-1)(71+1) = 71 « Previous topic | Next topic »
 Pages: 1 Reply Notify of replies Send Topic Print
 Author Topic: (71-1)(71+1) = 71  (Read 6729 times)
Grimbal
wu::riddles Moderator
Uberpuzzler

Gender:
Posts: 7408
 (71-1)(71+1) = 71   711.gif « on: Jul 31st, 2004, 11:44am » Quote Modify

Here is an equation: (71-1)(71+1) = 71

The astute reader will notice it is not true.

How can you make it a valid identity by adding
(a) a single dot
or (b) two dots
or (c) a single straight line.

Notes
1. For this problem, the 1 is a straight line, the 7 are 2 straight lines.
2. I want an IDENTITY.  Adding / on = is not an option.

[edit: change equation to identity]
 « Last Edit: Aug 1st, 2004, 7:32am by Grimbal » IP Logged

honkyboy
Junior Member

Gender:
Posts: 101
 Re: (71-1)(71+1) = 71   « Reply #1 on: Jul 31st, 2004, 4:06pm » Quote Modify

for a single dot (a)
(71-1)(71+1)=7!

A redundant dot could be added for two (not the intended answer I'm sure)
(71-1).(71+1)=7!
 IP Logged
Grimbal
wu::riddles Moderator
Uberpuzzler

Gender:
Posts: 7408
 Re: (71-1)(71+1) = 71   « Reply #2 on: Jul 31st, 2004, 4:26pm » Quote Modify

Even though I asked only one option, and this was the intended slution, on another forum we foud a solution for all 3 cases.

So keep searching.
 IP Logged
Sir Col
Uberpuzzler

impudens simia et macrologus profundus fabulae

Gender:
Posts: 1825
 Re: (71-1)(71+1) = 71   « Reply #3 on: Aug 1st, 2004, 3:55am » Quote Modify

If we don't have to state the base (4969), we could write (71-1)(71+1)[equiv]71?

It may just be semantics, but 3+4=7 is an identity, not an equation. An identity is true for all values, whereas an equation must contain a variable and is true for some, or none, of the values. For example, x=3, is an equation, because x need not always be 3; 3x+4x=7x is an identity, because it is true for all values of x.

So how about the equation... (71-L)(71+1)=71?
 IP Logged

mathschallenge.net / projecteuler.net
Grimbal
wu::riddles Moderator
Uberpuzzler

Gender:
Posts: 7408
 Re: (71-1)(71+1) = 71   « Reply #4 on: Aug 1st, 2004, 7:30am » Quote Modify

OK, ok,    I want an identity, then.
 IP Logged
Sir Col
Uberpuzzler

impudens simia et macrologus profundus fabulae

Gender:
Posts: 1825
 Re: (71-1)(71+1) = 71   « Reply #5 on: Aug 1st, 2004, 8:00am » Quote Modify

Sorry, I wasn't criticising.

I realised my "answer" wasn't what you were after, but I've been working on the single line part and I am still having difficulties. I don't suppose you would accept an inequality either... (71-1)(71+1)[ge]71?
 IP Logged

mathschallenge.net / projecteuler.net
Grimbal
wu::riddles Moderator
Uberpuzzler

Gender:
Posts: 7408
 Re: (71-1)(71+1) = 71   « Reply #6 on: Aug 1st, 2004, 2:15pm » Quote Modify

EQUALITY!  That is what I meant by equation.

So, no inequality either.
 IP Logged
Icarus
wu::riddles Moderator
Uberpuzzler

Boldly going where even angels fear to tread.

Gender:
Posts: 4863
 Re: (71-1)(71+1) = 71   « Reply #7 on: Aug 3rd, 2004, 9:32pm » Quote Modify

on Aug 1st, 2004, 3:55am, Sir Col wrote:
 3+4=7 is an identity, not an equation ... an equation must contain a variable

What? By the definitions I've always used, an equation is a statement of the form "A = B", where A and B are any valid expressions. 3+4=7 most certainly IS an equation, as is 3+4=89. The latter is false, but it is still an equation. There is no requirement that a variable be present. All that is required is that the statement equate two things.
 IP Logged

"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
towr
wu::riddles Moderator
Uberpuzzler

Some people are average, some are just mean.

Gender:
Posts: 13640
 Re: (71-1)(71+1) = 71   « Reply #8 on: Aug 4th, 2004, 12:21am » Quote Modify

Quote:
 http://mathworld.wolfram.com/Equation.html:   A mathematical expression stating that two or more quantities are the same as one another, also called an equality , formula , or identity .

 « Last Edit: Aug 4th, 2004, 12:22am by towr » IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
Sir Col
Uberpuzzler

impudens simia et macrologus profundus fabulae

Gender:
Posts: 1825
 Re: (71-1)(71+1) = 71   « Reply #9 on: Aug 4th, 2004, 3:25am » Quote Modify

I got all excited when I saw that someone had posted here, thinking they had found a solution to Grimbal's last question.

We've been down this road before, but...

Quote:
 http://en.wikipedia.org/wiki/Equation   In mathematics, one often (not quite always) distinguishes between an identity, which is an assertion that two expressions are equal regardless of the values of any variables that occur within them, and an equation, which may be true for only some (or none) of the values of any such variables. In equations, the values of the variables for which the equation is true are called solutions.

However, I checked in my (Collins) Mathematical Dictionary and it makes an interesting distinction...

Quote:
 Equation, n a formula that asserts that two expressions have the same value; it is either an identical equation (usually called an IDENTITY), which is true for any values of the variables, or a conditional equation, which is only true for certain values of the variables (the ROOTS of the equation). For example, x2-1=(x+1)(x-1) is an identity, and x2-1=3 is a conditional equation, with roots [pm]2.

In light of this, I concede that my original objection was a little pedantic. However, I've learned something new; and I don't mean that I am pedantic. (I already knew that!)
 IP Logged

mathschallenge.net / projecteuler.net
honkyboy
Junior Member

Gender:
Posts: 101
 Re: (71-1)(71+1) = 71   « Reply #10 on: Aug 4th, 2004, 11:17am » Quote Modify

 « Last Edit: Aug 4th, 2004, 11:18am by honkyboy » IP Logged
Grimbal
wu::riddles Moderator
Uberpuzzler

Gender:
Posts: 7408
 Re: (71-1)(71+1) = 71   « Reply #11 on: Aug 4th, 2004, 12:24pm » Quote Modify

A hint:
->The 2-dot solution is most likely to be found by a physicist...
The straight-line one more by ... well ... a typographer.
<-
 IP Logged
Leo Broukhis
Senior Riddler

Gender:
Posts: 459
 Re: (71-1)(71+1) = 71   « Reply #12 on: Aug 4th, 2004, 7:32pm » Quote Modify

on Aug 4th, 2004, 11:17am, honkyboy wrote:

I am not familiar with this notation. What do 4 dots mean? A missing element of a sequence?
 IP Logged
Leo Broukhis
Senior Riddler

Gender:
Posts: 459
 Re: (71-1)(71+1) = 71   « Reply #13 on: Aug 4th, 2004, 7:33pm » Quote Modify

Grimbal, are you implying an overbar?
 IP Logged
honkyboy
Junior Member

Gender:
Posts: 101
 Re: (71-1)(71+1) = 71   « Reply #14 on: Aug 4th, 2004, 7:37pm » Quote Modify

Four dot is for arithmetic mean.
4::6=5. the average of four and six is five.
 IP Logged
Grimbal
wu::riddles Moderator
Uberpuzzler

Gender:
Posts: 7408
 Re: (71-1)(71+1) = 71   « Reply #15 on: Aug 14th, 2004, 4:41pm » Quote Modify

(a) (71-1)(71+1) = 7!
(b) put a dot over the first 1 and over the second 71.
A dot is a derivation relative to time d/dt.  For constants, it is zero.

(c) (71-1)(71+1) = 71
or (71-1)(71+1) = 71

 « Last Edit: Aug 14th, 2004, 4:43pm by Grimbal » IP Logged
 Pages: 1 Reply Notify of replies Send Topic Print

 Forum Jump: ----------------------------- riddles -----------------------------  - easy => medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »