Math puzzles.

[rivka]

My father brought three math puzzles down with him this weekend. I got the first one pretty easily, struggled with the second, and had no chance in hell in getting the third. So I pass them all along you to guys.

1. Write the number 4 five times, in combination with any of the basic operators, to produce the sum of 55.

2. Take the numbers 2, 3, 4, and 5. Take any of the four basic operators - but you may only use each one once. Produce the sum of 26. Edited to add: You may not put two numbers next to each other to make a larger number (e.g., 25 + 4 -3). Treat them as separate integers.

3. Write the number 4 three times, employing any of a very broad set of mathematical operators, to produce the sum of 55.

Assume that there will be spoilers in the comments section.

Comments

Number 2

[hazelchaz]

24 + 5 - 3

[marnanel.livejournal.com]

I couldn't work out the last one, so I googled for it, and eventually found the answer. I wouldn't ever have got it.

[ailbhe]

Assuming I'm right in thinking "numbers" and "digits" are the same here - Rob got the first quickly 44+44/4 and I got the second quickly 25+4-3 but we're struggling on the third.

[wcg.livejournal.com]

I may come back and work on the first two later. For now, I offer this:

3. Write the number 4 three times, employing any of a very broad set of mathematical operators, to produce the sum of 55.

INT (e^4 + SQRT(4)/4) works out to INT(55.09) which is 55.

[kcobweb.livejournal.com]

answer to #2 (galagan figured this out, not me):
(5 + (3 / 2) ) x 4 = 26

[nolly.livejournal.com]

...you father listens to Car Talk, eh? (at least two of these have been on there recently.)

[(Anonymous)]

I have to say, I'm pretty impressed that you got the first one pretty easily - it took me longer than I liked.

The second was trivial - which I also found interesting, that you found it harder.

The third has been interesting... I've gotten a nonexistent answer ("and then plug 4 into the function that, for n an integer, f(n) returns the nth prime" (2, 3, 5, 7 - 7 is the fourth prime. And I can get to 48 pretty easily. But there's no way I can legitimately claim it's "any of a broad set of mathematical operators". Such a function *exists* - primes are well defined, and well ordered. But it's not a common function.)