Math Misery

@mathmisery.bsky.social

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Mathematician in Industry, Fractional Executive, Math Education https://HexSumGame.com --> post to #HexSumGame #gamedev #MTBoS #iTeachMath #mathsky #mathchat #datascience #machinelearning

Radius-2 daily HexSum puzzle. The board is set up in a honeycomb pattern tiled with hexagons with values read across the rows as
4, 1, 1
3, 4, 1, 1
2, 1, 10, 2*, 4*
2, 7, 3, 1*
1*, 1*, 1*

values with a * are part of a marked path adding to the center value of 10

Hand-drawn toy / cartoon monkey in a sitting pose with arms facing out and palms up.

Alt text: A trinomial recombining tree drawn as stacked rows of circles. The first row has one circle labeled 1. The second row has three circles labeled 1, 1, 1. The third row has five circles labeled 1, 2, 3, 2, 1. The fourth row has seven circles labeled 1, 3, 6, 7, 6, 3, 1. The fifth row has nine circles labeled 1, 4, 10, 16, 19, 16, 10, 4, 1. Each row expands outward in a triangular outline, and each circle is connected to three circles in the next row with plain line segments, showing recombination. To the right of the tree is a vertical column of math-style labels aligned with each row. The labels read (x^-1 + x^0 + x^1)^0 through (x^-1 + x^0 + x^1)^4, one expression per row, matching the five layers of the tree. The overall visual communicates a recombining trinomial expansion pattern, with the tree on the left and the matching math expressions on the right.

Blocks mode HexSum puzzle of radius 4, hexagon-tiled honeycomb pattern with values
[2, 3, 1, 3, 2]
[4, 5, 2, 1, 1, 1]
[2, 3, 3, 1, 4, 4, 7]
[8, 5, 2, 8, 6, 3, 2, 3]
[2, 2*, 3, 2, 10, 1, 2, 1, 1]
[3*, 7, 3, 4, 1, 6, 8, 1]
[1*, 2*, 2, 3, 4, 7, 1]
[2*, 3, 3, 6, 3, 1]
[1, 1, 4, 2, 1]

Values with asterisks next to them are part of the path given by the card in the top left corner. Other game modes and options are also shown.

Blocks mode puzzle for HexSum puzzles. Radius 4, honeycomb pattern tiled with hexagons. Values are

[2, 1, 3, 1, 3]
[3, 2, 3, 1, 3, 4]
[3, 1, 2, 2, 2*, 6, 1*]
[2, 1, 3, 3, 1*, 3*, 2*, 2*]
[3, 4, 6, 3*, 10, 2*, 4, 1*, 1]
[1, 5, 1*, 1, 3*, 1*, 1*, 2*]
[2, 2, 1*, 2*, 1*, 5*, 2*]
[4, 1*, 4, 3*, 4, 3*]
[4*, 1, 2, 4, 6]

Values with an asterisk next to them are part of a path as suggested by the card (top left).

Blocks mode puzzle for HexSum puzzles. Radius 4, honeycomb pattern tiled with hexagons. Values are

[2, 1, 3, 1, 3]
[3, 2, 3, 1, 3, 4]
[3, 1, 2, 2, 2*, 6, 1*]
[2, 1, 3, 3, 1*, 3*, 2*, 2*]
[3, 4, 6, 3*, 10, 2*, 4, 1*, 1]
[1, 5, 1*, 1, 3*, 1*, 1*, 2*]
[2, 2, 1*, 2*, 1*, 5*, 2*]
[4, 1*, 4, 3*, 4, 3*]
[4*, 1, 2, 4, 6]

Values with an asterisk next to them are part of a path as suggested by the card (top left).

Daily-2 HexSum puzzle shown as a honeycomb pattern tiled with hexagons. Values are
[2*, 5, 1]
[6, 7*, 2, 4]
[2, 1*, 10, 1, 7]
[4, 3, 3, 2]
[6, 1, 3]

The starred values are marked as a completed path on a dark brown background. The 10 is on an amber / gold background. All other values are on a white background.

The solved daily HexSum Blocks puzzle for 7/5/2026 found here: https://hexsumgame.com/blocks-daily/20260705

Radius 4, Daily Blocks puzzle mode at https://HexSumGame.com/blocks-daily

Values are
[6,1,7,2,3*]
[4,5,3,2,3*,1*]
[4,2,8,2,3*,2*,9]
[4,2,1*,2,1,2*,4*,1]
[1,1,3*,4*,10,2*,6*,1,1]
[1,2*,3*,7,3,2*,1*,6]
[2*,3,1,4,1*,3,7]
[7,1,3,3,2,3]
[3,3,2,1,3]

An asterisk following a value means it is part of a block as shown in the card on the top left. Other game modes and options are show, but the main focus is on the puzzle.

The Blocks puzzle available on weekends for logged out players at hexsumgame.com

The board is a radius 4, honeycomb tiled with hexagons.

Values across the rows are
[3, 5, 6, 4, 9]
[1, 2, 1, 8, 1, 6]
[1, 1, 8, 1, 2, 4, 3]
[1, 1, 1, 4, 1, 1, 4, 1]
[6, 1*, 1*, 1*, 10, 1, 1, 8, 2]
[5*, 2*, 6*, 2*, 3, 3, 1, 3]
[2*, 1*, 6, 2, 1, 1, 7]
[3*, 4*, 2, 2, 2, 3]
[7, 6, 2, 2, 1]

With the asterisk representing highlighted values for possible block selections. The block pattern is shown to the top left of the puzzle. Other game modes and options are visible.

A solved HexSum board. A radius 3, honeycomb pattern with four paths solving the board. The target sum is 10.

The daily Block-4 HexSum puzzle. Radius 4, honeycomb pattern with hex tiling. The values read

[1, 1*, 4*, 5*, 1*]
[4, 1, 3, 1, 3, 2]
[2, 2, 1*, 5*, 4*, 2, 5]
[1, 2, 5*, 1*, 4*, 4, 1, 1]
[1, 3, 8, 1, 10, 3, 2, 3, 1]
[4, 4, 4, 1, 2, 1,* 8*, 1*]
[1, 1, 1, 1, 1, 2, 3]
[4*, 3*, 3*, 1, 5, 3]
[1, 1, 1, 4, 1]

With asterisked values as parts of valid path choices as described by the three-tiled card on the top left

Daily-2 HexSum puzzle showing a hex-tiled honeycomb with values

[4,1,6]
[1,3,1,2]
[7,1,10,2,1]
[1,1,4,3]
[1,4,7]

The 10 is the target value on an amber / gold hex while all the other values are on white hexes.

Daily-2 HexSum. A honeycomb pattern tiled in hexagons that read across as follows:

[7,6,4]
[3,3,2,5]
[5,2,10,1,1]
[3,2,1,1]
[1,2,1]

The 10 is on a gold / amber background. The other hexes are on white.

The Blocks HexSum Daily puzzle for 6/21/2026 on a radius 4 honeycomb, hex-tiled board. The values are

[3,4,3,4,1]
[2,6,4,4,2,3]
[5,1,1,1,1*,1*,1]
[1,4,6,1*,3*,4*,3,3]
[4,1,3,1,10,5,3*,3*,1]
[1,1,7,7,1*,1*,2*,1]
[1,3,2*,4*,2*,4,2]
[3,3,3,1,2,2]
[1,9,1,1,2]

The values with asterisks next to them are part of paths that are possible paths to be placed given by the Block card shown in the top left.

Blocks puzzle mode for HexSum on a radius 4 board. Hex-tiled honeycomb pattern. Values are
[1*, 1*, 5, 1, 7]
[1, 1, 4*, 2, 2*, 4*]
[3, 5, 4*, 4, 6, 2, 1*]
[5, 5, 2, 4, 8, 2, 3*, 1]
[1, 2, 2, 3, 10, 2, 1, 4, 4]
[5, 1, 6, 1, 5, 1, 4, 6]
[2, 3, 1, 8, 1*, 4*, 4]
[2, 8, 1, 1, 8, 4*]
[6, 1, 1, 1, 1*]

Values followed by an asterisk are highlighted in purple as they are valid paths to select based on the card seen in the top left corner. Other game modes and options are displayed at the top.

Hard to describe beyond: sheet music for an unnamed composition. Key Bb for piano. 8 bar composition with a variation on the 8th measure for the second go around. A 9th bar to close out the piece.

Daily-3 HexSum puzzle. Honeycomb pattern tiled with hexagons. Values are

[1,2,2,1]
[1,6,1,1,3]
[1,4,6,6,4,3]
[1,5,7,10,2,1,1]
[5,2,3,1,1,6]
[1,8,2,2,1]
[1,2,1,5]

The target value of 10 is on a gold / amber background. The other values are on a white background. Other game modes (Daily-2, Daily-3, Daily-4, Daily-5, Timed-2, vs CPU, Blocks-4) and options (New Game, Social Share, Download) are visible as well as game interactions for (Undo, Play Again, Solve) and a general settings button.

HexSum Daily-3 puzzle in a honeycomb pattern tiled with hexagons.

The values read
[1,2,2,1]
[1,6,1,1,3]
[1,4,6,6,4,3]
[1,5,7,10,2,1,1]
[5,2,3,1,1,6]
[1,8,2,2,1]
[1,2,1,5]

The target value hexagon of 10 is on gold / amber color background. The other hexagons are on a white background

Daily-3 HexSum puzzle game. Hexagons tile a honeycomb pattern. The numbers on the hexagons are arranged as so

[4,1,1,3]
[3,1,4,1,2]
[1,1,2,1,2,8]
[2,1,1,10,3,5,2]
[1,3,3,3,3,3]
[1,3,7,1,3]
[8,2,9,1]

The daily-3 HexSum puzzle with one opening move show. The tiles are hexagons arranged in a honeycomb pattern. The values are
[2,1*,2,4]
[2,3*,6*,2,4]
[5,1,1,2,1,4]
[2,2,5,10,4,1,5]
[1,2,1,4,3,6]
[1,1,2,2,1]
[4,5,5,3]

The values with an asterisk next to them mark the values of the chosen path (background dark chocolate with an amber curve]. The 10 is on a gold / amber background. All other tiles are on a white background. Other game modes and puzzles are shown as well as game options.

The Daily-3 HexSum puzzle for 6/15/2026. Hexagon tiled honeycomb pattern with values reading across as
4,6,4,1
1,4,6,5,4
3,1,2,3,3,6
3,1,2,10,3,1,2
7,1,2,1,3,1
5,4,6,2,2
1,8,1,1

The target value 10 is in the center on a gold / amber background. All other hexes have a white background. Other puzzles and game mode options can be seen.

an example of a gerrymandered district. 54 squares in a 9x6 rectangle with alternating red / blue horizontal districts are gerrymandered into 5, 5/4 splits in favor of blue, and 1, 2/7 split in favor of red.

A radius-4 HexSum puzzle in a honeycomb pattern with hex tilings with a target value of 10.

The rows read across as
1,7,3,7,5
6,5,4,4,3,1
2,1,4,6,1,1,1
3,1,4,4,3,1,1,4
5,2,6,6,10,1,3,2,6
6,4,1,1,1,3,2,3
4,2,1,3,7,2,2
8,1,1,4,3,1
2,1,1,1,1

A radius-2 HexSum puzzle with a target value of 10. The main point of this image is to show the gear-settings development allowing players to use tap/drag selection and change how numbers are highlighted (dark/light).

The daily-3 HexSum puzzle. Hexagons tiling a honeycomb pattern. The values of the hexes across the rows read

[3,3,2,5]
[5,7,1,2,6]
[1,3,5,1,2,2]
[5,2,1,10,7,1,8]
[4,2,1,2,1,1]
[7,1,1,1,3]
[1,1,6,6]

The 10 is on a gold / amber hex while the others are in white.

Instructions read: Use all hexes and find paths that dd to the target value.

The daily-2 HexSum puzzle for 6/11/2026. The puzzle is in the shape of a honeycomb pattern tiled by hexagons. Reading across the hexes have values of [1,1,1][3,4,1,2][1,1,10,2,1][1,4,5,3][4,4,1]. The 10 is on a hex tile with a gold/amber background. The other hexes are colored white.

The daily-2 HexSum puzzle is shown as a radius 2 hex-tiled honeycomb. The hexes when read across the rows have values of [3, 8, 1][6, 1, 4, 1][5, 1, 10, 2, 3][5, 1, 3, 5][6, 1, 4]. The 10 is on an amber-colored hex tile. The other tiles are white in color. Other game modes are present.

The daily-2 HexSum puzzle is show. The puzzle is in a honeycomb pattern tiled by hexagons. The values on the hexagons read across rows as [1,7,4][7,2,6,6][2,3,10,4,8][5,2,3,2][1,2,5]. The hexagon containing the 10 is in gold / amber.

The daily-2 HexSum puzzle shown in a radius-2 honeycomb. Value reading across are [6,7,4][3,1,5,1][1,2,10,1,6][2,2,3,3][3,7,3]

A gold / amber colored arrow points to a button. The arrow is labeled "PDF".

The daily-2 HexSum puzzle is shown. It is a radius 2, flat-top, honeycomb pattern of hexagons. The rows read [3,2,1][4,5,2,3][2,2,10,1,2][8,2,3,3][3,3,1]. The target value, 10, is at the center on an amber background. The other hexagons are in white.

The daily radius 2, HexSum puzzle at https://hexsumgame.com/daily-2/20260606

A honeycomb hexagonal-tiling with values reading across as follows:
[2,1,2][5,1,2,1][2,4,10,1,1][1,3,4,2][1,1,6]

The center tile, 10, is in yellow.

A screenshot of a victory against the CPU in the HexSum game (hexsumgame.com). The victory was 32-31. In the background it can be seen that the player also completed all the daily puzzles.

A sample play of the HexSum game of player vs CPU in logged out mode. The CPU is winning 25-20. The player has found 4 solutions against the CPU's 5 solutions. It is the player's turn. The target sum is 30.

cover for "Mathematics and Chess" by Miodrag Petković

distribution of the largest cut of a piece string randomly cut into 20 pieces. the median is around 17% with a slight skew (mean > median).

abstraction of 40 pieces of string cut into 20 pieces

$continued fraction expansion of pi. 4/pi = 1 + 1^2/(2 + 3^2/(2 + 5^2/(2 + 7^2/(2 + ...))))$

adding in a term that allows for change in direction, we can find a stronger parametric fit, even with low sampled data

the logistic regression fit on actual data (unique actions taken vs conversion rate) shows strong correlation up to about 11 unique actions. beyond 11 unique actions there is a divergence between observation and fit.