Build a four-symbol grid with one of each per row and column

Write the two conditions above the empty grid

A four-symbol grid can have valid rows while its columns still fail. For this original paper activity, use four symbols, A, B, C and D, in a square with four rows and four columns. Put one symbol in each of its sixteen positions. The finished grid must contain each symbol exactly once in every row and exactly once in every column.

Those are the complete conditions for this exercise. The letters are written glyphs, not quantities, product codes or people assigned to a timetable. There is no requirement about diagonal lines or smaller boxes inside the square. We will construct one grid, inspect its columns and compare it with a version whose rows alone look correct.

Use an available sheet and a writing tool. Keep the conditions visible while filling the positions so that a familiar-looking square does not acquire extra rules halfway through the work.

Name positions before filling the first row

Number the rows one through four from top to bottom and the columns one through four from left to right. A label such as R2C3 means the position in row two, column three. These labels identify places on this particular page; they do not claim to be an application's address notation.

Begin with the first row reading A, B, C, D. It contains one copy of each permitted symbol. Keep that complete row visible as the starting sequence. Writing only a note saying that the row contains four letters would lose the particular order used for the construction.

Read the row aloud from its leftmost position to its rightmost. A should occupy R1C1, B R1C2, C R1C3 and D R1C4. If a symbol has been omitted or copied twice, correct the first-row copy before using it to produce later rows.

Move the leftmost symbol to the right end

To make the second row, take the first row's leftmost symbol A and move it to the right end of that sequence. Keep the other symbols in their existing order. The new row is B, C, D, A. This is a one-place left shift of the complete row, with the displaced symbol returning at the end.

Apply the same step to the second row to make the third. Move its leading B to the right end, leaving C, D, A, B. Then make the fourth row from the third by moving its leading C to the right end. The fourth row is D, A, B, C.

The complete grid therefore reads ABCD on row one, BCDA on row two, CDAB on row three and DABC on row four. The compact strings here stand for four separate symbols in four separate positions. They are not new four-letter symbols replacing the individual A, B, C and D.

Stop after the fourth row. Applying the shift once more would give ABCD again, but the declared square has only four rows. That additional sequence can stay in a separate working note; it is not another row to append to the finished sixteen-position grid.

Check what the construction preserves in each row

Moving the leading symbol to the end changes its position without creating or removing a symbol. Each of the four printed rows still contains A, B, C and D once. This checks the row condition for the construction you have actually written.

A copying mistake could still interrupt that method. For example, the second row should contain D in its third position, R2C3. Consult the complete BCDA sequence if that position is uncertain. Keep the intended row beside the written copy rather than filling a blank from an unstated pattern.

Do not conclude that the whole grid passes merely because every row has four different symbols. The column condition is separate. We will read each complete column of the finished grid next, using the same top-to-bottom direction throughout.

Read all four columns of the finished grid

The first column reads A, B, C, D from top to bottom. Its entries are the first symbols of the four rows. Each permitted symbol appears once, so column one passes. Marking the column checked records that particular sequence, not a general assumption about the other columns.

The second column reads B, C, D, A. The third reads C, D, A, B. The fourth reads D, A, B, C. Each of those three sequences also contains A, B, C and D exactly once. With the first column included, all four column checks are now explicit.

Keep the row strings and column strings together if someone else will review the activity. The row list shows how the page was built; the column list shows the second condition it satisfies. A reviewer can locate R2C3 as D in both the second row BCDA and the third column CDAB.

The agreement concerns the positions and symbols just printed. It does not measure a person's memory, visual ability or learning progress. Nor does it establish that a real set of physical pieces contains enough copies of each letter. Written copies supply the symbols for this authored paper exercise.

Compare a grid with four identical rows

On a separate working page, write ABCD four times, one copy per row. Every row now passes the row condition: each contains one A, one B, one C and one D. This makes a useful comparison because a row-only inspection would find no missing or repeated symbol within a row.

Read its first column. It is A, A, A, A. The other columns are B, B, B, B; C, C, C, C; and D, D, D, D. Every column fails the requirement to contain each of the four different symbols once.

The comparison shows why a complete row check cannot stand in for a complete column check. Keep the repeated-row page labeled as the failing example. Its rows have a property that the final activity requires, but that property alone does not satisfy the whole instruction.

Return to the shifted grid when presenting the completed construction. The two pages should remain distinguishable. Otherwise a reader may see a valid-row claim beside the wrong grid and have to guess whether the column failures were intentional.

Leave diagonal and smaller-box rules outside this activity

In the shifted grid, the diagonal from the top-left position to the bottom-right reads A, C, A, C. It repeats symbols. The other long diagonal reads D, D, D, D. Neither sequence contains all four symbols, and neither causes this grid to fail its stated row-and-column conditions.

The upper-left two-by-two block has A and B on its first row and B and C on its second. It contains B twice and no D. A rule requiring one of each symbol in that smaller block would therefore reject this particular construction. Such a rule has not been included in our exercise.

If you want to design an activity with additional diagonal or smaller-box conditions, state those conditions on a separate page and check a proposed grid against them. Do not describe the shifted grid as satisfying a requirement it visibly fails. Here its accepted result remains limited to the four complete rows and four complete columns.

Try a rearrangement that moves complete rows

Make another copy of the valid shifted grid and exchange its entire second and third rows. The new row order is ABCD, CDAB, BCDA, DABC. Every row keeps its own four symbols because you moved complete rows rather than altering their contents.

The new first column is A, C, B, D. Its symbols have changed order, but each still appears once. The same reasoning applies to every column: exchanging whole rows exchanges two positions within each column. It does not add a new symbol or remove an existing one from that column.

You can check the other new columns directly as B, D, C, A; C, A, D, B; and D, B, A, C. Each passes. This produces another valid arrangement under the same conditions without claiming that every possible valid grid has been listed.

This observation gives no permission to exchange arbitrary individual cells. A one-cell move can change the contents of both its row and its column. Keep the whole-row rearrangement identified as the particular change whose effect has been checked here.

Keep other grid questions separate

The row-and-column mismatch guide uses trusted numeric totals and a stipulated single changed entry. This activity constructs symbol arrangements. It has no saved numerical controls or guarantee identifying an unknown error in an actual table.

The display-pair counting guide uses row and column labels to name candidate image pairs. Here they identify positions, and each position holds one glyph. All sixteen positions remain in use; there is no diagonal exclusion or mirrored-pair counting rule.

Read the native paperweight references within their limits

The native Hotlips-Red account records an unknown brand. Two images show a red lips-shaped weight; one bears a Kosta Boda mark. That mark authenticates no manufacturer or material.

The native CC Gifts Dragonfly account has a brief description and one image of a faceted weight. Neither account supplies our grid rule.

Keep an order enquiry separate from the symbol checks

If you separately consider a paperweight order on republeq.com and want to ask about USDT, identify the actual offer and intended quantity before discussing payment. The letters and position labels in this activity are invented paper inputs, not product identifiers, checkout prices or cryptocurrency amounts. This article does not establish that a payment option is currently available for an account, location or basket. Read the choices and conditions actually presented for the intended transaction, and ask the responsible support contact to clarify essential information that remains missing. If a cryptocurrency option is offered, establish the specified asset and network, the requested amount, any stated validity period and the reference associating payment with that order. Do not infer a transfer destination from a paperweight photograph, a visible brand mark, an earlier transaction or a sequence of grid symbols. Keep the Hotlips account separate from the Dragonfly account when asking about the actual item and supplied contents. An answer about one does not automatically describe the other, and a changed quantity may require reviewing the resulting order information again. Ask separately about applicable delivery, cancellation, return and refund conditions, including how an approved amount would be determined, its denomination and any deductions. No present USDT eligibility, discount, conversion result, fee level, refund amount, processing time or delivery outcome is promised here. You can complete every grid check using an available sheet without ordering either weight. Preserve any eventual order acknowledgement and payment record separately from the letter activity. A correct row or column cannot authenticate a merchant's payment instructions, confirm an uncertain transaction or establish the material and origin of an offered object.

Save the finished grid with its actual conditions

Retain ABCD, BCDA, CDAB and DABC as the four original rows, with their four checked column sequences beside them. Keep the repeated-row failure and whole-row rearrangement as labeled comparisons. The construction satisfies one of each symbol per row and column; its repeated diagonals remain visible without being assigned an extra rule.