CT puzzle

Privacy policy: No personal information is collected by developer whilst users play CT Kids / CT Lite+, Touch CT, Chess CT (free with AdMob).

Touch CT is a logic rotational puzzle in 5x5 grid. Clues are the sums along horizontal, vertical, and two diagonals. Rotate as Rubik's cube to match sums at all four angles. Shake to restart after 1 minute. On App Store 3/6/2024 (version 1.0, self-advertisement). AdMob banner on top (ver. 2.0, on App Store 3/12/2024, replacing version 1.0). Google AdMob privacy policy (third-party advertisers and analytics may use coarse location, device id, usage data and diagnostics).

CT Lite (formerly CT Kids) is a logic 4x4 puzzle without rotation. Clues are the sums along x or y (horizontal or vertical direction). Shake to restart or reveal the answer after 30 sec. "Appropriate for kids" banner on top, version 1.1 on App Store 5/9/2024. First steps to integration: calculate sums over columns and rows (summing over sums over columns is equal to "find area under the curve"). Easy to solve: sums are visible all the time, turning red or green. CT Lite+ is on the App Store 2/27/2025. New (+) : Play, Make your own, Learn (create or copy/paste clues), beat the Timer on 5x5 "weighted" board.

Chess CT is a multi-level puzzle. Starting 4x4 board to 10x10. Rook and Bishop x-rays hidden pawns. Rotate as Rubik's cube (after few intro levels). No in-app purchases. Hints and answers at top levels. On App Store 6/13/2024 ← DOWNLOAD HERE. (now free with AdMob 10/18/2024)

CT Lite (formerly CT Kids)

Touch squares to match sums over columns and rows. No rotation.

CT Lite+ (upgraded CT Lite)

CT Lite used "Chess labeling": files are below, ranks on the left...

First, let's move "rank" clues to the right.

Next, let's assign values (a.k.a. "weights") to rows and columns.

Traditionally, values of the rows and columns appear on the left of and above the board. (That's why we moved our "rank" clues from left of the board to the right side.) When all values are equal, we are in "compatibility mode": e.g. at value=1 all clues are the same as were in CT Lite (formerly CT Kids).

Finally, an upgraded puzzle uses first 4 natural numbers as values for rows and columns: 1, 2, 3, 4 (making horizontal and vertical gradients).

Now each clue is the sum of weighted cells. E.g. in CT Lite+ the topmost row is 3 + 4 = 7 (not 1 + 1 = 2 as was in CT Lite). Player can easily distinguish between CT Lite and CT Lite+ by looking at the board labels (No values are in CT Lite. Progressive 1, 2, 3, 4 on top and on the left side — it is CT Lite+)

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Pattern satisfies all four projections

Touch CT and Chess CT rules: rotate and match the numbers at all angles

Touch squares to match numbers, remember numbers at other angles.

Numbers are the sum along "X-ray"

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Example: how to solve Touch CT

First, you can see 'X-rays'

Rotation buttons appeared instantly

step 1

Rotate clockwise (left button) and fill the column with 5. Then rotate counterclockwise twice (right button x2).

step 2

You can see now previously filled squares as a topmost row. Fill the middle column with 5. Rotate clockwise (left button).

step 3

Fill the diagonal with 4. Also fill the short (not main) diagonal with 3. Remember empty squares where is 0. Also point out that both short diagonals with 1s already matched numbers (they are green). Rotate clockwise again.

step 4

You can see that middle and leftmost columns already have matched sums. Keeping in mind 0 and 1 from previous step, you can figure out which square must be set in the column between them (the 2nd column from left). Rotate counterclockwise to satisfy the last red column.

step 5

There is only one way to set the last square. Solved!

Example: how to solve Touch CT (the same configuration as above, short way)

step 0 (what numbers you've get at start)

Look at numbers before pushing rotation buttons: you can fill short diagonal with 3. Also you can fill the diagonal with 4.

step 0b

Fill two diagonals, then rotate. Let's rotate clockwise (left button). We are going to see columns and rows.

step 1b

Fill the rightmost column to match 5. Rotate clockwise one more time.

step 2b

Fill the shortest diagonal with 2 and short diagonal with 3. Rotate clockwise again.

step 4b

Fill the middle column with 5. Done!

Another example (another random configuration) how to solve Touch CT

step 0

Fill diagonal with 3.

Rotate clockwise. (Of course, counterclockwise is valid too — and leads to the same solution: just another way, another series of steps)

step 1

look at image after rotation: vertical column with 5 can be filled.

step 1 (continue)

Fill the vertical column with 5.

Remember 4 for the middle vertical.

Rotate clockwise.

step 2

look at rotated image: diagonal with 2 already matched.

step 2 (continue)

Remembering 4 from previous step, set three squares.

step 2 (continue)

Fill the diagonal with 3

step 2 (continue)

Fill the diagonal with 4.

Remember 3 in main diagonal is not matched yet.

Rotate clockwise.

step 3

Set the last missed square in vertical with 4 (it matches diagonal 3 on previous step)

Puzzle has been solved!

done!

Just to verify solution — rotate to watch at all angles.

Strategic notes:

Rotate and look at numbers at all angles, hunting for 5s and 0s — filling 5 immediately and remembering "empties" make 0.
Finding 0 in row or column gives opportunity to fill 4s at perpendicular direction (if they exist there).
(at hard case) Calculate sum of diagonal numbers. It helps to determine are the corners empty.

one more example (it is on App Store in Touch CT preview)

... and one more (it's funny: symmetrical pattern)

Notes to the last example above:

(1) rotate to initial angle several times (when ^ pattern dominates) back and forth, CW and CCW;

(2) no 0s in this pattern!

Touch CT video example

short video (reel) on YouTube

Multilevel Chess CT

Rooks and bishops count hidden pawns

Three directions at this level: vertical, horizontal, and one diagonal.

Example: Chess CT (level 3)

initial position

need to match numbers for all three directions

here is the answer

advance to the next level

Example: How to solve Chess CT (level 4, rotational)

numbers at current angle visible only

step 0: fill the shortest diagonal with 2 pawns

rotate clockwise twice (left button x2)

remember 0 at the shortest diagonal

step 1: fill another shortest diagonal with 2

rotate clockwise, we are going to see columns and rows

keeping in mind 0 at previous step

step 2: set three pawns in rightmost column (skipping the square where was 0)

finally, rotate counterclockwise three times, moving to the initial angle

done!

step 3: fill the short diagonal with 2 pawns.

Advance to the next level (which is resemble Touch CT).

Less logical example: Chess CT (level 4, rotational)

Below are the numbers at every projection. Note: no 0s, no 4s. Pawns shown there for angle identification.

Here is the answer... And yet another answer! (We can call it "isometric variant"). Both satisfy initial numbers (check all angles).

Solving process:

step 1. Calculate sum along the rows (or columns). It is equal to 8. Then calculate the sums over diagonals. At one angle it is equal to 8, and at another angle it is equal to 6. Therefore: two corners are empty and two corners are having pawns.

(step 2 --- step last) will be published later... Since two variants are valid, one of the steps will include guess.

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