# Rama Math Help

These pages are to help people having problems with the alien number machines in the Sierra game Rama.

This page does not have the answers to the problems, it is to help you solve them. If you are using windows 95 there are instructions on how to use the calculator to do the math at the bottom of this page. Rama is to good a game to give up on because of the counting and math machines, that's why I made these pages.

If you have never used base 8 or 16 math before please read this entire page from top to bottom, don't skip the normal math section. Most people add and subtract from memory, without thinking about the rules for doing each. To do math in the other number systems you have to remember the rules you learned when you first started adding numbers with more than one digit in them. That is what the base 10 math section is for.

Think of the different number systems like they are different languages, not all languages use 26 letters like English, some have more, some (like Chinese) use symbols to represent whole words or phrases. Unlike languages, different number systems all use the same math rules. I've included examples of normal base 10 counting and math below so you can compare them to the examples in the base 8 and base 16 sections.

Without realizing it, most people know how to count in base 60. When ever you count seconds, minutes, and hours you are using base 60. If you've ever figured out how many seconds are in an hour you have converted a base 60 number to a base 10 number.

If you're still looking for what the symbols and colors on the machines mean, examine all 3 displays on the other side of each room. You may have to adjust your monitor to tell the last few colors apart in the octospider area.

### First let's review how our normal (base 10) number system works:

We have 10 digits: 0,1,2,3,4,5,6,7,8,9

Numbers are arranged in multiples of 10, so:

1111 is 1x10x10x10 + 1x10x10 + 1x10 + 1

When you count over 9 you add 1 to the next column in the number.

So adding 1 to 9, 19, 99, 199, and 999 gives 10, 20, 100, 200, and 1000

To add you carry a 1 when you go over 9, so: the addition of 1854+3638 would go like this:

1854
+3638

8+4=12 (You need to carry the 1)

3+5+1=9

6+8=14 (You need to carry the 1)

1+3+1=5

To subtract you need to move 10 over from the next column if the top number is smaller than the bottom number.|
The subtraction of 2362 from 8147 goes like this:

8147
-2362

7 - 2 = 5

4 is smaller that 6, you must subtract 1 from the next column and add 10 to 4:
1 - 1 = 0 and 10 + 4 = 14
14 - 6 = 8

0 is smaller that 3, you must subtract 1 from the next column and add 10 to 0:
8 - 1 = 7 and 10 + 0 = 10
10 - 3 = 7

7 - 2 = 5

### Now let's look at base 8, the number system used by the Octospiders.

They have 8 digits 0,1,2,3,4,5,6,7 which they represent with 8 colors.

Numbers are arranged in multiples of 8 so:

1111 is 1x8x8x8 + 1x8x8 + 1x8 +1 (in base 10)
Think of it this way, where we have tenths, hundredths, and thousandths, they would have eighths, sixty-fourths, and fivehundredtwelfths.

When you count over 7 you add 1 to the next column in the number.

So adding 1 to 7, 17, 77, 177, and 777gives 10, 20, 100, 200, and 1000

To add you carry a one when you go over 7, so: the addition of 1524+3637 would go like this:

1524
+3637

4 + 7 = 13 (carry the 1)

2 + 3 + 1 = 6

5 + 6 = 13 (carry the 1)

1 + 3 + 1 = 5

To subtract you need to move 10 over from the next column if the top number is smaller than the bottom number. (Keep in mind that's a 10 in base 8 that you move)
The subtraction of 2362 from 8147 goes like this:

6517
-3536

7 - 6 = 1

1 is smaller that 3, you must subtract 1 from the next column and add 10 to 1, this is where it's easy to get confused, remember, you're working in base 8:
5 - 1 = 4 and 10 + 1 = 11
11 - 3 = 6
To do this in base 10 on a simple calculator add 8 in the second step above and do the subtraction:
8 + 1 = 9 and 9 - 3 = 6   See, it's the same number.

4 is smaller that 5, you must subtract 1 from the next column and add 10 to 4:
6 - 1 = 5 and 10 + 4 = 14
14 - 5 = 7
To do this in base 10 on a simple calculator add 8 in the second step above and do the subtraction:
8 + 4 = 12 and 12 - 5 = 7

5 - 3 = 2

### Now for base 16, the number system used by the avians.

They have 16 digits, which makes it hard to write in our language.

For this explanation I am going to write each avian digit as 2 of our digits and separate them with a colin:

So their digits are: 01,02,03,04,05,06,07,08,09,10,11,12,13,14,15 which they represent with 15 symbols.

Remember each of these 2 digit numbers is a single digit in base 16.

Numbers are arranged in multiples of 16, so:

01:01:01:01 is 1x16x16x16 + 1x16x16 + 1x16 + 1 (in base 10)
Think of it this way, where we have tenths, hundredths, and thousandths, they would have sixteenths, 256ths, and 4096ths.

When you count over 15 you add 1 to the next column in the number.

So adding 01 to 15, 01:15, 02:15, 01:15:15, and 15:15:15 gives 01:00, 02:00, 01:00:00, 02:00:00, and 01:00:00:00

To add you carry a 1 when you go over 15, so: the addition of 10:09:14:03 + 03:06:11:08 would go like this:

10:09:14:03
+03:06:11:08

03 + 08 = 11

14 + 11 = 01:09 (carry the 01)

09 + 06 + 01 = 01:00 (carry the 01)

10 + 03 + 01 = 14

To subtract you need to move 10 over from the next column if the top number is smaller than the bottom number. (Keep in mind that's a 10 in base 16 that you move)
The subtraction of 01:14:09:05 from 06:14:01:10 goes like this:

06:14:01:10
-01:14:09:05

10 - 05 = 05

01 is smaller than 09, you must subtract 01 from the next colum and add 10 to the 01 (remember, that's a 10 in base 16 you're adding)
14 - 01 = 13 and 10 + 01 = 01:01
01:01 - 09 = 08
To do this in base 10 on a simple calculator add 16 in the second step above and do the subtraction:
16 + 1 = 17 and 17 - 9 = 8

13 is smaller than 14, you must subtract 01 from the next colum and add 10 to the 13:
06 - 01 = 05 and 10 + 13 = 02:03
02:03 - 14 = 15
To do this in base 10 on a simple calculator add 16 in the second step above and do the subtraction:
16 + 13 = 29 and 29 - 14 = 15

05 - 01 = 04

### How to use the Windows 95 calculator to solve the Rama math problems:

You should read the sections above to understand the what the different number systems are.

If you have enough available ram try starting the calculator before starting Rama. If you can get both to run, you can switch to the calculator while playing the game by pressing ALT-TAB. If you can't get both to run, you'll have to save your game, exit, use the calculator, and then restart the game.

The calculator must be in 'scientific mode' for these functions to work, to put the calculator in scientific mode click on 'View', and click on 'Scientific'.

The 3 modes you are going to use are DEC (base 10), HEX (base 16), and OCT (base 8). To switch modes you just click on the button next to the HEX, DEC, or OCT.

In OCT mode you can only use the 0-7 digits, and in HEX mode you use 0-9 and A-F to get the 15 digits. In HEX the digits 00-15 are 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F.

To convert from DEC to HEX or OCT just enter the number in DEC mode and press HEX or OCT, the number on the display will be converted.

To do math in any mode just enter the mode an use the calculator normally.

If you spot an error or have a suggestion please Email me.

Marty Schultz (schultz@science.widener.edu)