A number puzzle with 30-60-100

The golden ratio

Just simple arithmetic

Each of Matthew, Mark, and Luke in the New Testament hold different pieces of the sower’s puzzle in the three parallel accounts of the “Parable of the Sower.”  It is a story of someone who sows seed by scattering it here and there.  Here are the parts of the puzzle:

(1)  Matthew 13:8 – 100, 60, 30

(2)  Matthew 13:23 – 100, 60, 30

(3)  Mark 4:8 – 30, 60, 100

(4)  Mark 4:20 – 30, 60, 100

(5)  Luke 8:8 – 100

What to do with all these numbers?

I have pondered this puzzle, off and on, for a few years.  After much experimentation, this is what I came up with.

In the grid below, I have arranged the Matthew and Mark numbers, putting them around the center cell in the only way they will fit (other than the reverse).  I haven’t used all the numbers individually, but each set, (1) through (5), can be found displayed in the arrangement as in a crossword puzzle.  What to do with Luke’s lone 100?  Put it right in the center.


Arrangement of Numbers

In the Sower’s Puzzle











Adding up the columns, I get a total of 600.

So what?

Well, 600 is a special number.  The Greek letter that represents the number 600 is Chi (Χ).  That letter is also the first letter of the NT Greek word for Christ – Χριστός.

So we add up the numbers and see CHRIST!  Not a big thrill mathematically, but nice religious symbolism.

Notice that the arrangement has symmetry because the individual rows yield subtotals identical to those of individual columns.  I am tempted to add the rows and columns together to make a grand total of 600 + 600 = 1200.  Twelve hundred might have been a very meaningful number to those in the first century who found meaning in 12 apostles, 12 tribes of Israel, and 12 x 12,000 believers saved in Revelation.

Is it an error to read Matthew, Mark, and Luke together to combine elements to make a sower’s puzzle?  I don’t have a problem theorizing that all five elements were written and inserted in the books by the same hand.  We should consider the possibility that the books of the Gospel were written to be read together as a spiritual exercise and were in fact, read together; just as we read them together today.

Have I found the best possible solution to the sower’s puzzle in this post?  How can I be sure?  If only the meanings of Bible puzzles had been transmitted through the centuries!

But maybe there is no puzzle.  Maybe Mark just decided willy-nilly to write a number sequence twice.  Maybe Matthew just decided on a whim to reverse both.  Maybe Luke just forgot to write some numbers.  Maybe they didn’t know how to write concisely.  Maybe they didn’t know how to copy.

Or maybe they knew very well what they were doing!!!

Well, I kept thinking there might be more.  I kept having the urge to make this puzzle go three dimensional.

I tried various approaches for making a three-dimensional design.  Then I decided to make a cube.

Visualize this cube:

Each of six faces has the number arrangement in the grid above.  Each cell in the cube is three-dimensional now.  The cube has 27 three-dimensional cells.  The cell at the very center of the cube is blank.

The cube incorporates the same crossword puzzle theme as the grid above, that is, some numbers serve in multiple sets.  Example:  a corner cell which contains the number 30 is part of the six sets that converge at that corner.  The arrangement on each face has to be aligned (reversed if necessary) so that each corner has six convergences of the same number to complete the corner cell.

Cube surface showing alignment of its six faces.

What number to put in the blank center of the cube?

Luke has an interesting clue, “A crop, a hundred times more than was sown.”  Only Luke has “more than.” (Luke 8:8 (TNIV))  So for each seed sown, I get 100 more.

1 seed + 100 seeds = 101 seeds

I’m not going back to revise the first grid above since I like the way it worked out, and plain “100” is a valid choice there, but I will put “101” in the cube’s center cell.

Thus, the middle cross-section of the cube looks like this with numbers that add up to 741:


Middle Cross-Section

Of the Sower’s Puzzle Cube












 Sandwiching this middle cross-section are two side cross-sections that look like the first grid above and its reverse, each with numbers that add up to 600.

First, I add all the numbers within the cube front to back:

600 + 741 + 600 = 1941.

Then I add all the numbers within the cube left to right.  Same top to bottom.  Combine the three sums.  Because the cube has symmetry, this can be expressed as:

3 x 1941 = 5823

Then I sum all the numbers on the six faces of the cube:

6 x 600 = 3600

I divide that result into the previous sum:

5823 divided by 3600 = 1.6175 exactly.

The result is the golden ratio of 1.618 if you don’t mind rounding up.  Close enough for the first century?

I sure hope this is a solution because I sort of like it.

Update to the Sower’s Puzzle:  May 21, 2011

Another golden ratio

A symbol from Tibet

The Sower’s Puzzle goes four-dimensional

All simple arithmetic

I have to admit that as I add more steps to this Sower’s Puzzle, it gets increasingly unlikely that any biblical author would have envisioned it this way or that anyone has been this way before.  It would seem we are supposed to assemble numbers taken from the various sower parables in the Gospel.  Just where each person ends up with those numbers would depend on what path they take.

Of course, maybe there is no puzzle – only a meaningless bunch of numbers.  But I am going on the assumption that we are supposed to do something with the numbers.

I hope you can forgive me if I make the leap in logic that the environment for this puzzle is not just the New Testament but maybe also includes – Tibet?? !!!

In this post I bring in a symbol from Tibet.  I saw it on a flag at a Tibetan Buddhist temple on a DVD.  It is called the “Endless Knot.”

The Endless Knot, a Buddhist symbol

The Endless Knot (also, unending, eternal, or infinite knot) symbolizes “Buddha’s endless wisdom and compassion. It indicates continuity as the underlying reality of existence.” (  It doesn’t seem to matter if the symbol is turned 90 degrees.

Did Jesus ever visit Tibet to learn about Buddhism?  Well, I read recently that Buddhism did not reach Tibet until the seventh century CE.  Not for a thousand years?  How credible is that?  The Himalayas were in the way, yes.  But did it take a millennium?  Please!  And what about the symbol – did it originate in Tibet, India, or elsewhere?  I don’t believe anyone really knows where it came from originally or when it was devised, but apparently it is ancient.  Jesus and his biographer(s) did not live in an information vacuum and actually would not have needed to travel anywhere to be well informed.  They could have known about this symbol, if it existed at the time of Jesus in a place accessible to trade routes.

Even while I was developing the sower’s puzzle cube, I was looking for ways to launch it into the fourth dimension – time.  Maybe rotate it??  Maybe string cubes on a string??  I had no idea.

I started to think about the mathematical possibilities of doing a double cube, that is, taking the cube I already had, duplicating it, and joining two cubes end to end.  This results in a box-like shape.  The box is of equal width and depth, with the length twice the width.  Each cube has 27 three-dimensional cells; the box 54.  Ten of the cube faces still show.

I cast about in my mind for a way to represent the 10 visible faces on my double cube and thought of the Endless Knot symbol.  Now I had been pondering this symbol off and on for the much of the past year.  I had no idea what the symbol meant until I looked it up to draft this post, but I had guessed it might be used as some sort of meditation device.  I had discovered it is possible to draw this symbol without lifting pen from paper, without re-drawing a line segment, and by crossing lines (as in the “knot” drawing above) or alternatively, with no crossovers.  A way of focusing the mind?

Now considering the Endless Knot symbol once again, I realized with a jolt that it is composed of ten squares (yes, ten!), and the ten squares are not arranged just any which way, but actually are a graphic outline of the surface of a double cube!  The squares in the symbol are arranged so that if you have it on paper and cut the symbol out with scissors, you can fold up the paper surface into a double cube – if you are careful not to inadvertently snip off the dangling end squares.

There is something I like about this cubes-becoming-box and box-becoming-surface and surface-folding-up idea.  I like the feeling of movement; the openness in the design.  In the steps of building and disassembling and reinventing there is time – the fourth dimension.  There is a metaphor for Life.

So making the assumption that the Endless Knot could serve as a representation of the surface of my double cube, and that each square could hold a visible face of the cube, I populated the squares with sower’s cube numbers.  The faces being thus inserted have to be aligned so that matching numbers converge at corners and matching numbers meet at the seam between cubes.

Double-cube surface showing alignment of its ten faces

I also made the assumption that the lines in the Endless Knot symbol might function as a road map and if I followed the map, selecting numbers as I went along, I would gather up enough numbers to make a total I could use.  Interesting that no matter which way I traced out the map, using the different meditation routes I had discovered many months ago, the resulting total was the same – 3450.

I am going to spell out exactly which numbers I included so you will know.  There are 32 lengths between corners to traverse.  Start at the tiptop of the design.  Follow the pathway indicated by the “knot” drawing above.  Hint:  I did not count corner cells at the same map intersection twice.  (1) 30 60 100, (2) 60 30, (3) 60 100, (4) 60 30, (5) 60 100, (6) 60 30, (7) 60 100, (8) 60 30, (9) 60 100, (10) 60 30, (11) 60 100, (12) 60 30, (13) 60 100, (14) 60 30, (15) 60 100, (16) 60 30, (17) 60 100, (18) 60, (19) 60, (20) 60, (21) 60 100, (22) 60 30, (23) 60, (24) 60, (25) 60, (26) 60 30, (27) 60 100, (28) 60, (29) 60, (30) 60, (31) 60 100, (32) 60.    If you take a different route, the pattern will be different, but the total will presumably be the same – 3450.  It’s good I started with a “30” in the tiptop corner – a “100” there doesn’t give the same number.

Following a route through the symbol is not just counting; rather it is a kind of journeying.  It is like moving through a labyrinth.  Like moving through time.

Some numbers go missing when I use this method.  When I joined the cubes, the center 100’s in the joined faces didn’t show anymore.  Also the 101 cell at the very center of each cube is no more when I spread out the cube faces on a flat surface.

It did occur to me that in order to get the golden ratio in the milieu I set up, I needed 7200.  It just so happens that there is such a number in this puzzle, but I would have to go back in time to get it.  Well, that is just what I wanted – time travel!  A four-dimensional aspect to this puzzle!  So I go back in time to when I had two cubes, right before the moment I joined them together.  Two cubes, each cube with 6 faces, makes 12 faces.  The value of each face is 600:

12 x 600 = 7200

I should mention that “12” is also a number implied in the sower’s parables.  There are a total of 12 instances of seed scattered in various places by the sower among the three books of the Gospel that have this story.  So I feel justified in working with two cubes.

Now returning to the present moment, I find I have used every cell represented in the Endless Knot symbol at least once, except the center 100’s.  There are ten of them:

10 x 100 = 1000

I add that to my mapping number:

3450 + 1000 = 4450

Setting up a quotient I use my past and present numbers:

7200 divided by 4450 = 1.6179 . . . .

The result is the golden ratio of 1.618 if you don’t mind rounding up a bit.

By the way, the fourth dimension is there in the sower’s parables also.  The sower scatters the seed, and then waits to the end of the season to see what sort of crop develops.  As we hear this parable over and over three times, with only slight variation, we get a sense of déjà vu.  Haven’t we been here before?  As I work the puzzle likewise.  What?  The golden ratio again?

But what if there is no connection between the sower’s parables’ numbers and the Tibetan form?  What if it is historically impossible for them to have come from the same root?  Well, my proposed solution to my supposed puzzle is still interesting.  Why does it work?  Just a fluke?

My little vision quest doesn’t prove anything, but someone else might like to read this so I’ll put it up.

What is the fifth dimension?  Mind?  Spirit?

I have enjoyed this journey into my own mind.

7 Responses to SURREAL PUZZLE

  1. Human says:

    Incredible! Why does 101 deserve to be put in the center? What are the Greek letters that correspond to 101?

    • truleeyours says:

      Good question re deserving. When I needed a number for the only remaining space, it was the only remaining number specified (other numbers are implied). It worked.

  2. care4earth says:

    Have you considered the 30-60-90 degree triangle and what it might have to do with the Golden Mean?

  3. Human says:

    I like the Tibetan symbol. What does it symbolize?– Perhaps that time is endless and repeats itself??
    Another question: Why don’t you use the sum of 30 + 60 + 100 = 190? You might find the Golden Mean using 190.
    Keep on puzzling!

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