Math Game: Combining 4 Fours...

Factual Questions
1

Just wondering, has anyone been successful at building the numberline by using only math functions and the number 4? Let’s say, from 1-30. The simplest example: 4+4-4+4 = 0, for starters.
Are some numbers simply NOT possible to “create” in this fashion? (Yes, you can use factorials, exponents, etc…

It’s been awhile since I’ve thought about this. IIRC, I think 17 or maybe 23, as WAGs, might be such numbers. Hmm…what about the number “7”? That might be a tricky one, too.

Just wondering if other SDopers have played this game and what their findings are… - Jinx

2

7 = 4 + 4 - (4/4)
17 = 4 x 4 + (4/4)

3

OK, ok, ok …so, I am a little rusty! :wink:
What about 23 or 27?

  • Jinx
4

No.

Any number ‘n’ can be expressed as 1+1+1+1 … n times.

Simply represent that summation as (m+m+m+m …n times)/m.

5

I mean, integer of course, above, in place of number.

Any fraction is p/q. Which can be written as pm/qm.

Which is (m+m+m…p times)/(m+m+m…q times)

6

23 = 4! - (4)^(4-4)
27 = 4! + 4 - 4/4

7

Although I’ve already answered, your example confuses me.

Either it’s wrong or I haven’t understood your query in the first place.

You could simply write 4-4 = 0. In fact, your example resolves to 8, not 0.

8

Gyan9, I think you misunderstood. You must use exactly 4 4’s.

23 = [symbol]Ö[/symbol](4! - 4/4)[sup][symbol]Ö/symbol[/sup]

9

There are two functions by which many of the familiar functions can be constructed. They are Z(x) defined by Z(x) = 0, and N(x), given by N(x) = x + 1. Given these two functions, it’s quite easy to map 4 onto any natural number.

To wit: 0 is Z(4), 1 is N(Z(4)), 2 is N(N(Z(4))), and so forth.

10

I don’t think factorial is allowed, after all, it’s just a shorthand for muliplying a whole bunch of numbers.

11

Depending on which actions you decide to allow, you can easily go up into the triple digits. I wasted a lot of time on time many, many years ago.

12

How do you define 4! without writing 1,2,3 ?

13

Youch…triple post!

1 = 4/44/4
2 = 4/44/[symbol]Ö[/symbol]4

Can we use recurring decimals? Taking .4’ to mean .4444444…,

3 = (4 + 4)/(4[symbol]Ö/symbol)

14

1 = 4/4
2 = (44)/(4+4)
3 = (4+4+4)/4
4 = (44)-(4+4)
5 = ((44)+4)/4
6 = 4+4+4/(sqrt(4)) (ok, i cheated here :-P)
7 = 4+4-(4/4)
8 = (44-4)-4
9 = 4+4+(4/4)

15

Every other time I’ve seen this problem, the allowable operations were all things that a middle schooler could reasonably be expected to know, and nothing that involved writing other numbers or letters (i.e., just notation using non-alphanumeric symbols).

Using this guideline, I’ve seen lists going all the way up to 112. I haven’t seen one for 113.

16

10 = 4/.4*4/4
11 = 44/([symbol]Ö/symbol)
12 = 4! - 4 - 4 - 4
13 = 4! - 44/4

17

Ooops…forgot to go back and change my 1.

18

14 = 4 + 4 + 4 + [symbol]Ö[/symbol]4
15 = 4*4 - 4/4

19

16= 4!- 4-4
17 = 4*4+(4/4)

20

Blew it on 16. Should be:

16 = 4+4+4+4