The Lemon Fool

An old puzzle asks you to express a number using four 4s using only addition, subtraction, multiplication, division, square roots, factorial sign and power. For example

9 = 4 + 4 + 4/4
40 = (4^4)/4 – 4!

But can you express 64 using only two 4s?

Cinelli

must be easy if I can get it

sqr(4)x4

NT

cinelli wrote:

An old puzzle asks you to express a number using four 4s using only addition, subtraction, multiplication, division, square roots, factorial sign and power. For example

9 = 4 + 4 + 4/4
40 = (4^4)/4 – 4!

But can you express 64 using only two 4s?

Cinelli

Spoiler:


sqrt(sqrt(sqrt(4^4!)))

Sorry can't say much about my method except that I fugured it would be easier to work only with powers of 2, since 64 is a power of two.

NearlyThere wrote:must be easy if I can get it

sqr(4)x4

NT

Unfortunately squares are not allowed, only square roots!

GS

GoSeigen wrote:
Sorry can't say much about my method except that I fugured it would be easier to work only with powers of 2, since 64 is a power of two.

Not merely easier, absolutely necessary. 4^4 is too big, and no other simple combo using the allowed operators comes close. So you need some more complex formulation, and you simply considered what could be done without introducing non-powers of 4.

I guess there's also a clue in the slightly-idiosyncratic list of allowed operators.

Reply to GoSeigen:

Excellent solution! I thought that was a hard puzzle.

Cinelli

cinelli wrote:Reply to GoSeigen:

Excellent solution! I thought that was a hard puzzle.

Cinelli

I found it easier than some you post, so interested to see what others think. Maybe different minds work in different ways?

My kids are struggling with it.



GS

GoSeigen wrote:

cinelli wrote:Reply to GoSeigen:

Excellent solution! I thought that was a hard puzzle.

Cinelli

I found it easier than some you post, so interested to see what others think. Maybe different minds work in different ways?
GS

Perhaps an analogy here is in order (it came to mind when I made my previous comment on GS's solution).

When I first encountered the "magic cube" - later known as Rubik's cube - I was just starting out as a maths student and treated it as a practical exercise. And of course come the summer hols, I also showed it to others I knew elsewhere.

One such was particularly memorable: my young cousin, aged 5 at the time, who was keen to have a go. I gave her some 'interesting' puzzles, based on setting up nice symmetric patterns, and watched. I was impressed by her approach: she didn't solve it on the spot, but she did make a lot of moves that very sensibly preserved that symmetry. Much better than the average monkeyperson.

I see the same sensible approach in GS's post. And with this being a much smaller problem space, I'll agree with him it's easier than an average cinelli. Though I didn't solve it myself: there's been no place for such puzzles in my life these past four months or so.