come back with puzzle

distance · #1 $Old$ 10-31-2008, 12:55 AM

Live is like a puzzle !

You are equipped with a single 2, 3, 23, and 32 along with the ability to combine them using addition, subtraction, multiplication, division, and exponentiation.

Your job is to create all of the integers from 33 to 50 (inclusive).

You may use any number of parentheses to control the order of operations and need not use all four numbers each time. Remember, no number can be used twice.

For example: 24 = 32 - 2^3
(where 2^3 means 2 to the 3rd power)

Obsidantion · #2 $Old$ 10-31-2008, 07:22 AM

Nice puzzle.

33 = 32 - 2 + 3
34 = 32 + 2
35 = 32 + 3
36 = (32 / 2) - 3 + 23
37 = 32 + 3 + 2
38 = 32 + (3 x 2)
39 = ((23 - 2) / 3) + 32
40 = (2 ^ 3) + 32
41 = (3 ^ 2) + 32
42 = 32 + ((23 - 3) / 2)
43 = (23 x 2) - 3
44 = (32 x 2) - 23 + 3
45 = ((23 + 3) / 2) + 32
46 = 23 + 32 - (3 ^ 2)
47 = 23 + 32 - (2 ^ 3)
48 = 32 x 3 / 2
49 = 23 + 32 - (2 x 3)
50 = 23 + 32 - 2 - 3

Soroban · #3 $Old$ 10-31-2008, 12:43 PM

Hello, distance!

I got most of them . . . How far did you get?

Quote:

You are equipped with: 2, 3, 23, and 32 along with the ability to combine them
using addition, subtraction, multiplication, division, and exponentiation.

Your job is to create all of the integers from 33 to 50 (inclusive).

You may use any number of parentheses to control the order of operations
and need not use all four numbers. .No number can be used twice.

$\begin{array}{c|c} 33 & \quad32 + (3-2) \\ 34 & \quad32 + 2 \\ 35 & \quad32 + 3 \\ 36 & \quad23 + \frac{32}{2} - 3 \\ 37 & \quad32 + 2 + 3 \\ 38 & \quad32 + (2\times3) \\ 39 & \quad--- \\ 40 & \quad32 + 2^3 \\ 41 & \quad32 + 3^2 \\ 42 & \quad 23 + \frac{32}{2} + 3 \end{array}$
$\begin{array}{c|c} 43 & --- \\ 44 & (32\times2) - (23-3) \\ 45 & 32 + \frac{23+3}{2} \\ 46 & (23+32) - 3^2 \\ 47 & (23+32) - 2^3 \\ 48 & --- \\ 49 & (23+32) - (3\times2) \end{array}$
$\begin{array}{c|c}50 & (23+32) - (2+3) \end{array}$

masters · #4 $Old$ 10-31-2008, 01:03 PM

$39=\frac{23-2}{3}+32$

$43=2(23)-3$

$48=\frac{32}{2} \times 3$

distance · #5 $Old$ 10-31-2008, 01:40 PM

You solved it...Great job