Category Archives: Brain

Use a 6-sided dice as a 4-sided or 5-sided dice

In my previous posts on this subject, I have show how to use a 6-sided dice to create a 2-sided, a 3-sided, an 8-sided or even create a 12-sided dice. Today I will show how to use a 6-sided dice to create a 4-sided or 5-sided dice.

Turn a 6-sided dice as a 5-sided dice:
Roll the 6-sided dice, and if you roll a 6, roll again. Do this till you roll a value between 1 and 5. Pretty simple.

Turn a 6-sided dice as a 4-sided dice:
Method 1:
Roll the 6-sided dice, and if you roll a 5 or 6, roll again. Do this till you roll a value between 1 and 4. Pretty simple.

Method 2:
Roll a 6-sided dice. The top of the dice will be ignored — we care about the four sides, not the top. On the four sides there are four values. The lowest value maps to 1, the second lowest value maps to 2, the next highest value is 3 and finally, the highest of the four values is 4. Whichever is facing you is the roll (just map it to the range 1..4). Rank the side facing you among the four sides, and you have created a four sided dice from a six-sided one. Note: If a side is not facing you squarely, turn the dice to the left so that the that side is facing you squarely.

For example, let’s say you roll a 6-sided dice, and the top face showing is the 5. That means that the four sides are { 1, 3, 4, 6 } — and the value of 2 is on the bottom. Of the four sides, one is most facing you. If it is the 6 most facing you, then your answer is 4 because 6 is the 4th of the four numbers on the four sides; it is the largest of the four side values, which are: {1, 3, 4, 6}.

How to roll a 6-sided dice once and generate a number from 1 to 8

One roll of a six-sided die can be used to generate any number from 1 to 6 (with an equal chance for each of the six). Likewise, I found a way to randomly generate any number from 1 to 8 with one roll of a six sided die (with an equal chance for each of the eight). When you roll a six sided dice, you will be able to see three faces and three faces only — the top and two sides. That is, don’t move from where you sit, and you will be able to see three sides! Of course, if you move around, you can see the other sides. I am talking about you, the dice roller, keeping your head still.

From where you sit (and not moving your head), observe the three faces you can see. Add up the numbers from the three faces you see, and you will get one of the eight possible sum totals:


For example, if you see faces with the numbers 6, 5 and 3 then your total is 14. If you see 1, 4 and 2 then your total is 7. All that is needed is a way to map these eight possible sums to the numbers 1 through 8. For that, I have the following table:

1: 11
2: 12
3: 9
4: 14
5: 15
6: 6
7: 7
8: 10

If the sum of the sides is 10, the value you generated is 8. If the sum of the faces is 14, then the value you generated is 4. There is pattern here: generally, the last digit of the sum is the value generated. For example, 11 has 1 as the last digit, so 11 maps to 1. If your faces add up to an 11, you rolled a 1. Likewise, 14 has 4 as the last digit, and hence maps to 4. The only exceptions are 9 (which maps to 3) and the sum of 10 which maps to 8. All the other numbers map nicely to the last digit. Note that 3 squared is 9, so that may make it easy to remember. And 10 is the only number left with nothing to do, so corresponds to rolling an 8.

Edge Cases
What if you can only see two faces on a roll? This is a case where the dice lines up squarely in your vision. In this event, lean slightly to the right and pick up the third face — the key here is that you always lean to right as a rule. Because it is a rule, you are never preferring one face over the other.

Prove It
Each of the eight values are equally likely to show up because there are eight corners on a cube. Each of those corners has three faces touching it. Our random number generator — using a six-sided dice to generate values 1 to 8 — works because we are rolling in such a way as to access one of these eight corners. If we rolled so that the 2 is showing on top, we will see two more faces (to the left and right): either {1 and 3} as the two sides, or {3 and 6} or {6 and 4} or {4 and 1}. In this case, each corner has a unique sum, and each corner can turn up in one of three ways. Following this method, every possible combination for all possible corners was listed and shown that all eight are uniquely matched to a particular sum, and each is evenly distributed.

Your six sided dice is many sided! See my other post on how to roll a six-sided dice to get other random values. All told, a six sided dice can be used as a 6-sided, an 8-sided, or as a 12-sided dice, or as a 3-sided or a 2-sided dice. Can you discover more?


Playing Cards without a Deck of Cards

This is Part I of my Head Games system of card playing. It is a system for card games using a standard deck of cards, yet played without an actual deck.  I am developing the system, and decided to present it now and see what others are doing and if I can get ideas for expanding what can be done with this.

Stated Simply
Is it possible to play cards without cards?  The answer is yes! I will show you how to work with a random deck of 52 cards, and give a way of selecting cards from that deck with any number of people playing.

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11 Ways to Make Your Brain Stronger

Our brains can be exercised and can improve through the right methods. We can change how we think, and we can improve our capacity to remember.  And there are definite techniques that can help. There are secrets you can learn that really do work (and I am not selling anything!).

Are you skeptical? Don’t believe me? Well, you may not be alone in your skepticism, but new tools, old tools and new studies all point to one wonderful reality: We can train our brain. We can work it out as in the fitness center, and come away with more strength.

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The Day the Universe Changed

When change happens — change that we adopt as a culture — it updates the features of our society. In fact, change itself is part of what defines us. New features become part of our lives and then refocus our view of the world.  For example, the discoveries of science shape how we think and interact with our environment. How would we understand life and society without the intimate experience of light bulbs, cell phones, glasses, jet planes, televisions, guns and laptops? To name just a few.

James Burke is the master of developing the ramifications of change, technology and the attending impact on our beliefs and actions.  When I was 15 he came out with a ten-part series of shows titled The Day the Universe Changed.  And I was changed.   I forgot how much his work impacted me.   I was reflecting on his presentation style and his ability to connect information and I realized that in my own PhD work I am mimicking him! Certainly not consciously, for it just occurred to me that such is the case, but the case none the less.

I have a high regard for Dr. Burke and want to direct you to the foundational series on You Tube:

That is only one of his videos. Many of his episodes are viewable on YouTube (search there for, “The Day the Universe Changed”). A research project he leads is Knowledge Web. Finally, I would be terribly remiss if I did not direct you to the excellent series that started it all: Connections.

I used to sit with great awe and soak in this material. Based on a fresh review, I assure you that it has not lost its power.

Steve Rives
Louisburg, Kansas