Using the digits 1, 2, 3, 4 develop a mathematical formula for every number between..

[wiggly]

My daughter was given an extra credit asignment with the following problem:

Your mission, should you choose to accept it, is to create 100 different equations. Each equation must equal a different number from 1 to 100. The answers to these equations have been written in the grid for you.
THE RULES: You MUST use the digits 1, 2, 3, and 4 in each equation. You MAY NOT use any other digits (0, 5, 6, etc.) You must use each digit (1-4) once and only once in the equation. For example, you MAY use 1+2+3+4, but NOT 1+1+2+3+4, and NOT 1+2+3 You may NOT create 2 digit numbers. For example: no 12 or 23

Has anyone had this and solved it or is it impossible?

 

[wiggly]

>Each equation must equal a different number from 1 to 100.
>The answers to these equations have been written in the grid for you.

What does that mean? What grid?

Anyway, if only + - * / are allowed, then maximum is 4 * 3 * 2 + 1 = 25.
Anything else allowed? Like 3^4 = 81 ?

No limits on the type of equation. The grid was just a sheet that the teacher included for the answers.

 

[stapel]

No limits on the type of equation.

So it is not true that only addition, subtraction, multiplication, and division are allowed? Other things, like grouping, powers, roots, factorials, etc, are allowed? Can one use anything one has heard of, or is there some expanded listing of allowed operations?

Please be specific. Thank you!

 

[wiggly]

The only specific instrustions are that you can only use a digit once in the equations.

 

[Steven G]

My daughter was given an extra credit asignment with the following problem:

Your mission, should you choose to accept it, is to create 100 different equations. Each equation must equal a different number from 1 to 100. The answers to these equations have been written in the grid for you.
THE RULES: You MUST use the digits 1, 2, 3, and 4 in each equation. You MAY NOT use any other digits (0, 5, 6, etc.) You must use each digit (1-4) once and only once in the equation. For example, you MAY use 1+2+3+4, but NOT 1+1+2+3+4, and NOT 1+2+3 You may NOT create 2 digit numbers. For example: no 12 or 23

Has anyone had this and solved it or is it impossible?

{[(1)^2]^3}^4 = 1. Now permute the 2,3 and 4 to get 3! =6 eqs. 4/3/2/1 and (4/3)*(2/1) are two more. Just keep going....

 

[Steven G]

Delayed xmas gift:
(3^SQRT(4) + 1)^2 = 100 :cool:

With "anything goes" being the rule, the decimal point may be used; example:
4 / .2 * 3 + 1 = 20 * 3 + 1 = 61

Good luck.

I was waiting to see how you would go with 'anything goes' but I think that using .2 is taking this a bit too far.

 

[wiggly]

Almost there...

With a lot of work and a little help, my daughter and I have completed all but two of the problems. We are stuck on solving for the numbers 85 and 86. Any ideas?

 

[Deleted member 4993]

With a lot of work and a little help, my daughter and I have completed all but two of the problems. We are stuck on solving for the numbers 85 and 86. Any ideas?

Shouldn't you let your daughter solve those problems - for her extra credits??

 

[Ishuda]

With a lot of work and a little help, my daughter and I have completed all but two of the problems. We are stuck on solving for the numbers 85 and 86. Any ideas?

Are you using the decimal point idea?
86 = 2 * (4/.1 + 3)

 

[wiggly]

43 * 2 - 1 = 85
43 * 2 * 1 = 86

We have to use the numbers 1, 2, 3 and 4 only

 

[wiggly]

Are you using the decimal point idea?
86 = 2 * (4/.1 + 3)

I think we have to use the decimal points to complete this

 

[wiggly]

Shouldn't you let your daughter solve those problems - for her extra credits??

She has but the teacher is only giving extra credit if all the number equations are solved.

 

[Steven G]

I think we have to use the decimal points to complete this

It is very unusual that I would defend Dennis but if you can use .1 (which is NOT 1) then why can't you use 43?

 

[Steven G]

She has but the teacher is only giving extra credit if all the number equations are solved.

But that is exactly Subhotosh's point! Your daughter should do it and if she can't then she doesn't get the extra credit.

 

[wiggly]

Did I mention that this was for seventh grade math?

 

[soroban]

I too have nothing against using decimal points.

I found: \(\displaystyle \:86 \:=\:\dfrac{3!}{.1} + 4! + 2\)

 

[lookagain]

The expression for 86, which appears in the first line below, can be formed, in part, using decimal points
and without using any factorial signs:


\(\displaystyle \boxed{ \ 2(4 \ + \ .3)/.1 \ } \ \) =

\(\displaystyle 2(4.3)/.1 \ = \)

\(\displaystyle 8.6/.1 \ = \)

\(\displaystyle 8.6(10) \ = \)

\(\displaystyle 86\)

 

[Deleted member 4993]

Very neat Sir LA!

With the "unclear rules" assuming anything goes:

SUM(1 + ..... + 3!) * 4 + 2 = 86

If I was a teacher and a grade 7 student gave me this,
I'd give 100% plus a red star!

..... Not allowed !!

 

[Steven G]

I just have to say that you folks are just brilliant. My mind is just not opened as much as yours.

 

[Steven G]

Very neat Sir LA!

With the "unclear rules" assuming anything goes:

SUM(1 + ..... + 3!) * 4 + 2 = 86

If I was a teacher and a grade 7 student gave me this,
I'd give 100% plus a red star!

I am trying to imagine Dennis as a 7th grade mathteacher. Since I always believe that students come first I can't joke about this one -darn. It would be refreshing to know that someone competent with mathematical talent was teaching this class.
It is sad that over the years my weakest students have always been math education majors (and business majors)