From last week’s New Scientist

Find mathematical combinations using the numbers 9, 16 and 22 each exactly once to form the integers from 1 to 10.

You are allowed to + – / and * and can square or square root as often as you want.

For instance: (22+9^0.5)^0.5-16^0.5 = 1

I managed to get everything except 5, then looked up the answer and found I could have got 5 as well with another few weeks of thinking about it.

sibeen said:

Although thinking about it,

may have been easier :)

sibeen said:

Alternate:

sibeen said:

I’ll be really pissed off if you get 5 quickly.

sibeen said:

I’ll be really pissed off if you get 5 quickly.

nerd

The Rev Dodgson said:

From last week’s New Scientist

Find mathematical combinations using the numbers 9, 16 and 22 each exactly once to form the integers from 1 to 10.

You are allowed to + – / and * and can square or square root as often as you want.

For instance: (22+9^0.5)^0.5-16^0.5 = 1

I managed to get everything except 5, then looked up the answer and found I could have got 5 as well with another few weeks of thinking about it.

So you’ve given us 1.

(22-16)/sqrt(9) = 2

(22-16) – sqrt(9) = 3

(22-16)^2/9 = 4

9^2 – 22*sqrt(16) = 7

22/sqrt(sqrt(16))-sqrt(9) = 8

((22-16) – sqrt(9))^2 = 9

22 – sqrt(9)*sqrt(16) = 10

Need a bit more time on 5 and 6

dv said:

The Rev Dodgson said:

From last week’s New Scientist

Find mathematical combinations using the numbers 9, 16 and 22 each exactly once to form the integers from 1 to 10.

You are allowed to + – / and * and can square or square root as often as you want.

For instance: (22+9^0.5)^0.5-16^0.5 = 1

I managed to get everything except 5, then looked up the answer and found I could have got 5 as well with another few weeks of thinking about it.

So you’ve given us 1.

(22-16)/sqrt(9) = 2

(22-16) – sqrt(9) = 3

(22-16)^2/9 = 4

9^2 – 22*sqrt(16) = 7

22/sqrt(sqrt(16))-sqrt(9) = 8

((22-16) – sqrt(9))^2 = 9

22 – sqrt(9)*sqrt(16) = 10

Need a bit more time on 5 and 6

I got 6 pretty quickly.

The other one that took me longer was 4, where I ended up with: 22-(9*(16^0.5)^0.5)

The Rev Dodgson said:

From last week’s New Scientist

Find mathematical combinations using the numbers 9, 16 and 22 each exactly once to form the integers from 1 to 10.

You are allowed to + – / and * and can square or square root as often as you want.

For instance: (22+9^0.5)^0.5-16^0.5 = 1

I managed to get everything except 5, then looked up the answer and found I could have got 5 as well with another few weeks of thinking about it.

I’ll get back to you in a fortnight.

The Rev Dodgson said:

dv said:

The Rev Dodgson said:

From last week’s New Scientist

Find mathematical combinations using the numbers 9, 16 and 22 each exactly once to form the integers from 1 to 10.

You are allowed to + – / and * and can square or square root as often as you want.

For instance: (22+9^0.5)^0.5-16^0.5 = 1

I managed to get everything except 5, then looked up the answer and found I could have got 5 as well with another few weeks of thinking about it.

So you’ve given us 1.

(22-16)/sqrt(9) = 2

(22-16) – sqrt(9) = 3

(22-16)^2/9 = 4

9^2 – 22*sqrt(16) = 7

22/sqrt(sqrt(16))-sqrt(9) = 8

((22-16) – sqrt(9))^2 = 9

22 – sqrt(9)*sqrt(16) = 10

Need a bit more time on 5 and 6

I got 6 pretty quickly.

The other one that took me longer was 4, where I ended up with: 22-(9*(16^0.5)^0.5)

I mean … if you’ve got 2, it’s pretty easy to get to 4…

dv said:

The Rev Dodgson said:

dv said:

So you’ve given us 1.

(22-16)/sqrt(9) = 2

(22-16) – sqrt(9) = 3

(22-16)^2/9 = 4

9^2 – 22*sqrt(16) = 7

22/sqrt(sqrt(16))-sqrt(9) = 8

((22-16) – sqrt(9))^2 = 9

22 – sqrt(9)*sqrt(16) = 10

Need a bit more time on 5 and 6

I got 6 pretty quickly.

The other one that took me longer was 4, where I ended up with: 22-(9*(16^0.5)^0.5)

I mean … if you’ve got 2, it’s pretty easy to get to 4…

Depends how you got 2 :)

dv said:

The Rev Dodgson said:

dv said:

So you’ve given us 1.

(22-16)/sqrt(9) = 2

(22-16) – sqrt(9) = 3

(22-16)^2/9 = 4

9^2 – 22*sqrt(16) = 7

22/sqrt(sqrt(16))-sqrt(9) = 8

((22-16) – sqrt(9))^2 = 9

22 – sqrt(9)*sqrt(16) = 10

Need a bit more time on 5 and 6

I got 6 pretty quickly.

The other one that took me longer was 4, where I ended up with: 22-(9*(16^0.5)^0.5)

I mean … if you’ve got 2, it’s pretty easy to get to 4…

s’pose so, now you mention it :)

Wait, have I assumed too much in thinking brackets are free?

sibeen said:

dv said:

The Rev Dodgson said:

I got 6 pretty quickly.

The other one that took me longer was 4, where I ended up with: 22-(9*(16^0.5)^0.5)

I mean … if you’ve got 2, it’s pretty easy to get to 4…

Depends how you got 2 :)

I’m pretty sure that
(however you got 2)^2

will always work.

The Rev Dodgson said:

sibeen said:

dv said:

I mean … if you’ve got 2, it’s pretty easy to get to 4…

Depends how you got 2 :)

I’m pretty sure that
(however you got 2)^2

will always work.

True dat.

sibeen said:

noice

dv said:

sibeen said:

noice

So only 5 to solve now :)

(needs lots of rooting)

I don’t think I can afford to let this nerdsnipe me, I could easily end up spending hours on this if I don’t watch me step.

dv said:

I don’t think I can afford to let this nerdsnipe me, I could easily end up spending hours on this if I don’t watch me step.

Why should I be the only one :)

The Rev Dodgson said:

dv said:

I don’t think I can afford to let this nerdsnipe me, I could easily end up spending hours on this if I don’t watch me step.

Why should I be the only one :)

Hold on, hold on, you stated that you looked up the answer!!!!!!!!!

sibeen said:

The Rev Dodgson said:

dv said:

I don’t think I can afford to let this nerdsnipe me, I could easily end up spending hours on this if I don’t watch me step.

Why should I be the only one :)

Hold on, hold on, you stated that you looked up the answer!!!!!!!!!

But only after spending a week thinking about it!

Did you ever do the four fours?

What is the smallest integer you can get using just for fours?

Apparently, there is no such smallest integer. All integers can be constructed using just four fours. I didn’t figure that out, but I have (or used to have) a book that gives the method.

Oops.
Did you ever do the four fours?

What is the smallest integer you can’t get using just for fours?

Apparently, there is no such smallest integer. All integers can be constructed using just four fours. I didn’t figure that out, but I have (or used to have) a book that gives the method.

Fixed.

The Rev Dodgson said:

sibeen said:

The Rev Dodgson said:

Why should I be the only one :)

Hold on, hold on, you stated that you looked up the answer!!!!!!!!!

But only after spending a week thinking about it!

sqrt(22 + sqrt(9)) = ?

mollwollfumble said:

Did you ever do the four fours?

What is the smallest integer you can get using just for fours?

Apparently, there is no such smallest integer. All integers can be constructed using just four fours. I didn’t figure that out, but I have (or used to have) a book that gives the method.

Be very interested to hear about that

mollwollfumble said:

Did you ever do the four fours?

What is the smallest integer you can get using just for fours?

Apparently, there is no such smallest integer. All integers can be constructed using just four fours. I didn’t figure that out, but I have (or used to have) a book that gives the method.

We did the four fours on SSSF. I think Magic Chook introduced it.

btm said:

The Rev Dodgson said:

sibeen said:

Hold on, hold on, you stated that you looked up the answer!!!!!!!!!

But only after spending a week thinking about it!

sqrt(22 + sqrt(9)) = ?

Where’s the 16?

dv said:

btm said:

sqrt(22 + sqrt(9)) = ?

Where’s the 16?

Sorry, I didn’t read the original question. Ignore my answer.

mollwollfumble said:

Oops.
Did you ever do the four fours?

What is the smallest integer you can’t get using just four fours?

Apparently, there is no such smallest integer. All integers can be constructed using just four fours. I didn’t figure that out, but I have (or used to have) a book that gives the method.

Fixed.

What operations are allowed?

btm said:

mollwollfumble said:

Oops.
Did you ever do the four fours?

What is the smallest integer you can’t get using just four fours?

Apparently, there is no such smallest integer. All integers can be constructed using just four fours. I didn’t figure that out, but I have (or used to have) a book that gives the method.

Fixed.

What operations are allowed?

Kind of seems like an absurd claim. There are surely only a finite number of arithmetic expressions involving four fours.

btm said:

The Rev Dodgson said:

sibeen said:

Hold on, hold on, you stated that you looked up the answer!!!!!!!!!

But only after spending a week thinking about it!

sqrt(22 + sqrt(9)) = ?

You have to use the 16 as well.

dv said:

btm said:

mollwollfumble said:

Oops.
Did you ever do the four fours?

What is the smallest integer you can’t get using just four fours?

Apparently, there is no such smallest integer. All integers can be constructed using just four fours. I didn’t figure that out, but I have (or used to have) a book that gives the method.

Fixed.

What operations are allowed?

Kind of seems like an absurd claim. There are surely only a finite number of arithmetic expressions involving four fours.

… but there do seem to be several ways of getting 1:

44/44
(4^4)/(4^4)

etc

dv said:

btm said:

mollwollfumble said:

Oops.
Did you ever do the four fours?

What is the smallest integer you can’t get using just four fours?

Apparently, there is no such smallest integer. All integers can be constructed using just four fours. I didn’t figure that out, but I have (or used to have) a book that gives the method.

Fixed.

What operations are allowed?

Kind of seems like an absurd claim. There are surely only a finite number of arithmetic expressions involving four fours.

Almost infinite you mean

The Rev Dodgson said:

dv said:

btm said:

What operations are allowed?

Kind of seems like an absurd claim. There are surely only a finite number of arithmetic expressions involving four fours.

… but there do seem to be several ways of getting 1:

44/44
(4^4)/(4^4)

etc

Right but moll is saying you can use four fours to get to any integer.
1231, -107212, any integer.

dv said:

The Rev Dodgson said:

dv said:

Kind of seems like an absurd claim. There are surely only a finite number of arithmetic expressions involving four fours.

… but there do seem to be several ways of getting 1:

44/44
(4^4)/(4^4)

etc

Right but moll is saying you can use four fours to get to any integer.
1231, -107212, any integer.

If I remember correctly, it was the integers 1 to 100.

dv said:

The Rev Dodgson said:

dv said:

Kind of seems like an absurd claim. There are surely only a finite number of arithmetic expressions involving four fours.

… but there do seem to be several ways of getting 1:

44/44
(4^4)/(4^4)

etc

Right but moll is saying you can use four fours to get to any integer.
1231, -107212, any integer.

Yeah, I agree with you on that bit.

sibeen said:

dv said:

The Rev Dodgson said:

… but there do seem to be several ways of getting 1:

44/44
(4^4)/(4^4)

etc

Right but moll is saying you can use four fours to get to any integer.
1231, -107212, any integer.

If I remember correctly, it was the integers 1 to 100.

Surely 1 is the lowest, whatever the upper limit is.

The Rev Dodgson said:

sibeen said:

dv said:

Right but moll is saying you can use four fours to get to any integer.
1231, -107212, any integer.

If I remember correctly, it was the integers 1 to 100.

Surely 1 is the lowest, whatever the upper limit is.

Oh, I probably should read the question.

Smallest you can’t get.

I suppose this will end up being a laborious search among combinations of 5^32, 22^4 etc

This was part of a test NASA gave me before I could do consulting work for them, knocked it out in about 10 minutes

dv said:

I suppose this will end up being a laborious search among combinations of 5^32, 22^4 etc

Yeah, just been on a run and that’s what I was thinking.

I think I might have to admit defeat

dv said:

I think I might have to admit defeat

It’s good to know your limitations but be aware I will have less respect for you even if that doesn’t seem possible.

dv said:

I think I might have to admit defeat

I’ll allow sibeen another alf our, then I’ll post the answer.

The Rev Dodgson said:

dv said:

I think I might have to admit defeat

I’ll allow sibeen another alf our, then I’ll post the answer.

never give him the answer…

The Rev Dodgson said:

dv said:

I think I might have to admit defeat

I’ll allow sibeen another alf our, then I’ll post the answer.

I’ve been fiddling around with it, but I’ll throw my towel in with deevs.

Arts said:

The Rev Dodgson said:

dv said:

I think I might have to admit defeat

I’ll allow sibeen another alf our, then I’ll post the answer.

never give him the answer…

You’re a cruel, cruel woman.

sibeen said:

The Rev Dodgson said:

dv said:

I think I might have to admit defeat

I’ll allow sibeen another alf our, then I’ll post the answer.

I’ve been fiddling around with it, but I’ll throw my towel in with deevs.

OK, well here it is then:

(22+((9^((16^0.5)^0.5))^0.5)^0.5)^0.5 = 5

The Rev Dodgson said:

sibeen said:

The Rev Dodgson said:

I’ll allow sibeen another alf our, then I’ll post the answer.

I’ve been fiddling around with it, but I’ll throw my towel in with deevs.

OK, well here it is then:

(22+((9^((16^0.5)^0.5))^0.5)^0.5)^0.5 = 5

sibeen said:

The Rev Dodgson said:

sibeen said:

I’ve been fiddling around with it, but I’ll throw my towel in with deevs.

OK, well here it is then:

(22+((9^((16^0.5)^0.5))^0.5)^0.5)^0.5 = 5

Sorry, misread the brackets.

Should have been able to get that.

sibeen said:

The Rev Dodgson said:

sibeen said:

I’ve been fiddling around with it, but I’ll throw my towel in with deevs.

OK, well here it is then:

(22+((9^((16^0.5)^0.5))^0.5)^0.5)^0.5 = 5

Should be:

sqrt(22+sqrt(sqrt(9^sqrt(sqrt(16)))))

sibeen said:

Should have been able to get that.

That’s what I thought when I saw it.

Anyway, glad that you and dv didn’t get it either :)

Rev, I considered that kind of option, but it’s kind of outside the scope of the puzzle as stated.

“You are allowed to + – / and * and can square or square root as often as you want.”

It doesn’t say you’re allowed other exponentiation.

I’m displeased.

dv said:

Rev, I considered that kind of option, but it’s kind of outside the scope of the puzzle as stated.

“You are allowed to + – / and * and can square or square root as often as you want.”

It doesn’t say you’re allowed other exponentiation.

I’m displeased.

**

dv said:

Rev, I considered that kind of option, but it’s kind of outside the scope of the puzzle as stated.

“You are allowed to + – / and * and can square or square root as often as you want.”

It doesn’t say you’re allowed other exponentiation.

I’m displeased.

Where is the other exponentiation? It’s all just repeated square rooting.

The Rev Dodgson said:

dv said:

Rev, I considered that kind of option, but it’s kind of outside the scope of the puzzle as stated.

“You are allowed to + – / and * and can square or square root as often as you want.”

It doesn’t say you’re allowed other exponentiation.

I’m displeased.

Where is the other exponentiation? It’s all just repeated square rooting.

it’s this operator you can’t see here

SCIENCE said:

The Rev Dodgson said:

dv said:

Rev, I considered that kind of option, but it’s kind of outside the scope of the puzzle as stated.

“You are allowed to + – / and * and can square or square root as often as you want.”

It doesn’t say you’re allowed other exponentiation.

I’m displeased.

Where is the other exponentiation? It’s all just repeated square rooting.

it’s this operator you can’t see here

You are right.

I can’t see any operator between the 9 and the square root symbol.

9 to the power of the square root of the square root of 16 = 81.

The Rev Dodgson said:

SCIENCE said:

The Rev Dodgson said:

Where is the other exponentiation? It’s all just repeated square rooting.

it’s this operator you can’t see here

You are right.

I can’t see any operator between the 9 and the square root symbol.

9 to the power of the square root of the square root of 16 = 81.

so are you agreeing that the inflection or pitch or tonality of an expression has an impact on the meaning of the expression, or are you agreeing that it doesn’t

SCIENCE said:

The Rev Dodgson said:

SCIENCE said:

it’s this operator you can’t see here

You are right.

I can’t see any operator between the 9 and the square root symbol.

9 to the power of the square root of the square root of 16 = 81.

so are you agreeing that the inflection or pitch or tonality of an expression has an impact on the meaning of the expression, or are you agreeing that it doesn’t

I wasn’t making any comment on that statement.

The Rev Dodgson said:

SCIENCE said:

The Rev Dodgson said:

You are right.

I can’t see any operator between the 9 and the square root symbol.

9 to the power of the square root of the square root of 16 = 81.

so are you agreeing that the inflection or pitch or tonality of an expression has an impact on the meaning of the expression, or are you agreeing that it doesn’t

I wasn’t making any comment on that statement.

I’m sure you can see it. It may not be represented by a symbol: it’s represented by position.
But I’m not even talking about symbols. I’m talking about operations . We would assume that the list of allowed operations was an exhaustive list.

dv said:

The Rev Dodgson said:

SCIENCE said:

so are you agreeing that the inflection or pitch or tonality of an expression has an impact on the meaning of the expression, or are you agreeing that it doesn’t

I wasn’t making any comment on that statement.

I’m sure you can see it. It may not be represented by a symbol: it’s represented by position.
But I’m not even talking about symbols. I’m talking about operations . We would assume that the list of allowed operations was an exhaustive list.

right but if we(1,1,1)’re going to get all technical then instead of stuff like

surely yous’d be better off writing them as for instance

sqrt(add(22,sqrt(sqrt(pow(9,sqrt(sqrt(16)))))))

and then the discussion could continue on whether pow was an appropriate operation

dv said:

The Rev Dodgson said:

SCIENCE said:

so are you agreeing that the inflection or pitch or tonality of an expression has an impact on the meaning of the expression, or are you agreeing that it doesn’t

I wasn’t making any comment on that statement.

I’m sure you can see it. It may not be represented by a symbol: it’s represented by position.
But I’m not even talking about symbols. I’m talking about operations . We would assume that the list of allowed operations was an exhaustive list.

But where is the operation that isn’t a square or square root?

SCIENCE pointed out 9^2, so it can’t be that one.

dv said:

The Rev Dodgson said:

SCIENCE said:

so are you agreeing that the inflection or pitch or tonality of an expression has an impact on the meaning of the expression, or are you agreeing that it doesn’t

I wasn’t making any comment on that statement.

I’m sure you can see it. It may not be represented by a symbol: it’s represented by position.
But I’m not even talking about symbols. I’m talking about operations . We would assume that the list of allowed operations was an exhaustive list.

But where is the operation that isn’t a square or square root?

SCIENCE pointed out 9^2, so it can’t be that one.

The Rev Dodgson said:

dv said:

The Rev Dodgson said:

I wasn’t making any comment on that statement.

I’m sure you can see it. It may not be represented by a symbol: it’s represented by position.
But I’m not even talking about symbols. I’m talking about operations . We would assume that the list of allowed operations was an exhaustive list.

But where is the operation that isn’t a square or square root?

SCIENCE pointed out 9^2, so it can’t be that one.

ah so it’s a semantic metapuzzle now is that it

SCIENCE said:

The Rev Dodgson said:

dv said:

I’m sure you can see it. It may not be represented by a symbol: it’s represented by position.
But I’m not even talking about symbols. I’m talking about operations . We would assume that the list of allowed operations was an exhaustive list.

But where is the operation that isn’t a square or square root?

SCIENCE pointed out 9^2, so it can’t be that one.

ah so it’s a semantic metapuzzle now is that it

If you want.

Personally I’d rather just put some brackets around (sqrt(sqrt(16)) to turn in into 2, then 9^2 is clearly allowed under the stated conditions.

The Rev Dodgson said:

SCIENCE said:

The Rev Dodgson said:

But where is the operation that isn’t a square or square root?

SCIENCE pointed out 9^2, so it can’t be that one.

ah so it’s a semantic metapuzzle now is that it

If you want.

Personally I’d rather just put some brackets around (sqrt(sqrt(16)) to turn in into 2, then 9^2 is clearly allowed under the stated conditions.

well all right we’d have to see the original Act or Constitution to be sure, rules are rules, there are operators like square(.) and there are effects

SCIENCE said:

The Rev Dodgson said:

SCIENCE said:

ah so it’s a semantic metapuzzle now is that it

If you want.

Personally I’d rather just put some brackets around (sqrt(sqrt(16)) to turn in into 2, then 9^2 is clearly allowed under the stated conditions.

well all right we’d have to see the original Act or Constitution to be sure, rules are rules, there are operators like square(.) and there are effects

Oh, we’ve moved on from discussing operations to operators have we?

Luckily the original conditions are stated in the opening post, which says you can square, which I have always understood to be raising to the power 2, often indicated these days with ^2.

I’ll be writing to the ombudsman.

dv said:

I’ll be writing to the ombudsman.

Shouldn’t you give New Scientist the chance to explain themselves first?

The Rev Dodgson said:

dv said:

I’ll be writing to the ombudsman.

Shouldn’t you give New Scientist the chance to explain themselves first?

I assume I will not be the only punter less than grunted. There are difficult puzzles, then there are puzzles that are just poorly framed.
Maybe next week they’ll ask for three words ending in gry.

dv said:

The Rev Dodgson said:

dv said:

I’ll be writing to the ombudsman.

Shouldn’t you give New Scientist the chance to explain themselves first?

I assume I will not be the only punter less than grunted. There are difficult puzzles, then there are puzzles that are just poorly framed.
Maybe next week they’ll ask for three words ending in gry.

That would be in New English.

dv said:

The Rev Dodgson said:

dv said:

I’ll be writing to the ombudsman.

Shouldn’t you give New Scientist the chance to explain themselves first?

I assume I will not be the only punter less than grunted. There are difficult puzzles, then there are puzzles that are just poorly framed.
Maybe next week they’ll ask for three words ending in gry.

Next time I’ll be sure to post on the approved day for pedantic discussions.

The Rev Dodgson said:

Oh, we’ve moved on from discussing operations to operators have we?

Luckily the original

well as you can see there’s been no moving on to have or otherwise, both have been discussed at length

SCIENCE said:

The Rev Dodgson said:

Oh, we’ve moved on from discussing operations to operators have we?

Luckily the original

well as you can see there’s been no moving on to have or otherwise, both have been discussed at length

Why were you discussing operators at length?

The Rev Dodgson said:

SCIENCE said:

The Rev Dodgson said:

Oh, we’ve moved on from discussing operations to operators have we?

Luckily the original

well as you can see there’s been no moving on to have or otherwise, both have been discussed at length

Why were you discussing operators at length?

probably inspired by this thread or something

SCIENCE said:

The Rev Dodgson said:

SCIENCE said:

well as you can see there’s been no moving on to have or otherwise, both have been discussed at length

Why were you discussing operators at length?

probably inspired by this thread or something

But that seems to say that you can square as often as you want, so I’m really not understanding why a solution that includes a square operation should be disputed.

The Rev Dodgson said:

SCIENCE said:

The Rev Dodgson said:

Why were you discussing operators at length?

probably inspired by this thread or something

But that seems to say that you can square as often as you want, so I’m really not understanding why a solution that includes a square operation should be disputed.

Is -1 included in all that square rooting?

Peak Warming Man said:

The Rev Dodgson said:

SCIENCE said:

probably inspired by this thread or something

But that seems to say that you can square as often as you want, so I’m really not understanding why a solution that includes a square operation should be disputed.

Is -1 included in all that square rooting?

Fortunately we only need to root positive values, so we can forget about all that imaginary nonsense.

The Rev Dodgson said:

Peak Warming Man said:

The Rev Dodgson said:

But that seems to say that you can square as often as you want, so I’m really not understanding why a solution that includes a square operation should be disputed.

Is -1 included in all that square rooting?

Fortunately we only need to root positive values, so we can forget about all that imaginary nonsense.

I’m with you pilgrim.
I woke up to them years ago when they suddenly out of nowhere slipped the square of -1 into the an equation to make it work thinking no one would notice.
They thought we were mugs.

mollwollfumble said:

Oops.
Did you ever do the four fours?

What is the smallest integer you can’t get using just for fours?

Apparently, there is no such smallest integer. All integers can be constructed using just four fours. I didn’t figure that out, but I have (or used to have) a book that gives the method.

Fixed.

I’ve started having a look at this for integers between 1 and 100.

The only way I can get even close is if I allow powers of 0, 0.5, 2 and 3.

Allowing that I’ve got up to 52, except for 43.

In particular, to get even close I need to be able to get 1 using just one 4, so needed 4^0.

Is there a name for raising to the power 0, so I don’t need the 0?

you can name any operation you choose

SCIENCE said:

you can name any operation you choose

In that case I can generate any integer you like with just one four.

SCIENCE said:

you can name any operation you choose

In that case I can generate any integer you like with just one four.

The Rev Dodgson said:

SCIENCE said:

you can name any operation you choose

In that case I can generate any integer you like with just one four.

similarly, but without any four