# How can I use 4, 4, and 4 to result in the number 31?

1. Sep 23, 2004

### turkldo

How can I use 4, 4, and 4 to result in the number 31? You can perform any operation the 4's, but you can only use three 4's.

2. Sep 23, 2004

### jcsd

bah! I can do it with only 2 4's:

[cosh(4) + 4] = 31

3. Sep 23, 2004

### A_I_

what do u mean by cosh.. i didn't understand the h?

4. Sep 23, 2004

### turkldo

You are required to use all three of the 4's. I should have been more specific...sorry.

5. Sep 23, 2004

### turkldo

AI,

JCSD used the Hyperbolic Cosine function.

The cosh function operates element-wise on arrays. The function's domains and ranges include complex values. All angles are in radians.

Y = cosh(X) returns the hyperbolic cosine for each element of X.

Now, cosh 4 = 27.308

6. Sep 23, 2004

### A_I_

how can we do it on a calculator.. i mean the cosh.. or does it have any formula?

7. Sep 23, 2004

### Tide

$$\cosh x = \frac {e^x + e^{-x}}{2}$$

8. Sep 23, 2004

### turkldo

I have a TI-85. On it you select 2nd, Math. Next you press F4 for the HYP menu. Then you choose the type of hyperbolic function you want to use.

9. Sep 23, 2004

### Chrono

Or you could just type in (e^x + e^-x)/2

10. Sep 23, 2004

### JasonRox

4^0 + 4^0 ... + 4^0 = 31

Technically I didn't use any four's since it is exponent 0.

It is possible I know that.

You have many options to work with.

11. Sep 23, 2004

### recon

Is this a brain teaser or a question you found in a mathematics textbook?

12. Sep 23, 2004

### Tide

$$4^{4-\sqrt 4} = 31$$

... base 5! :-)

13. Sep 24, 2004

### gazzo

Oooh. Does this count?

$${\lfloor}\int_{4}^{4+4} cosh (\theta + \theta + \theta){\rfloor}$$

14. Sep 24, 2004