Paper indicator memory: the same input can keep either color

Paper indicator memory explains why two records can finish with the same input number and different colors. In the invented worksheet below, input three keeps the color that was present immediately before it. A blue ending and an orange ending can therefore both follow the rule. Check the preceding state before correcting either record.

The actual Earthborn Elements baking powder offer names a resealable 3.5-gallon bucket and a 400 Ounce Pack of 1. Those are separate statements in its retail account. They are not a mass-to-volume conversion established here.

The Fleischmann's baking powder offer names YY-ERPO-1243, ten pounds per container and four containers per case. Its photograph shows one labelled container. That photograph does not independently establish the complete delivered quantity.

These ingredient offers are optional shopping references, separate from the paper exercise. Its input numbers are not temperatures, amounts, times or ingredient readings. Its colors do not describe food. Nothing below tests either powder, gives a recipe or establishes a product's condition.

Write the complete paper rule before following a record

Use a page with one box for an indicator color. The only permitted colors are BLUE and ORANGE. Write one of them in the box before starting. That written color is the indicator's current state. Neither color means good, bad, safe, ready or faulty in this exercise.

The allowed inputs are the five labels one, two, three, four and five. Each step supplies exactly one input. Apply its rule to the current color, then record the resulting color before proceeding. An input is a number on the page; a state is the color written in the box.

Here is the entire rule. Input one or input two sets the indicator to BLUE. Input four or input five sets it to ORANGE. Input three leaves the indicator at its previous color. These are stipulated instructions for this worksheet, with no additional behavior left for the reader to infer.

Setting a color may leave the written word unchanged. If the box already says BLUE, input one still produces BLUE. Likewise, input five produces ORANGE when the box already says ORANGE. A step can follow its rule without producing a visible change.

Apply one input at a time. Finish writing the resulting color before reading the next input. You are tracing one indicator through a supplied sequence, using the color from the preceding step.

Choose the initial color explicitly. For a worked record that starts ORANGE, write ORANGE on its first line before listing inputs. For a separate record that starts BLUE, write BLUE. Leaving that entry blank would leave the outcome of an initial three unresolved under the stated rule.

Read the middle input rule before changing the color

The middle input rule says to keep the previous color when the input is three. Three is not another name for BLUE or ORANGE. It selects an instruction that needs the current color as well as the input number. Read both entries before writing the result.

Start the first worked record at ORANGE. Supply input one. The rule sets the indicator to BLUE, so write BLUE beside that input. Now supply input three. Immediately before this second step, the color is BLUE. Keeping that color produces BLUE again.

The complete first record reads: start ORANGE; input one, result BLUE; input three, result BLUE. The starting ORANGE was replaced at the first step. The later three keeps BLUE because BLUE is the state present just before that three. It does not recover the record's starting color.

For a second, independent record, start at BLUE. Supply input five, which sets the indicator to ORANGE. Then supply input three. Immediately before that three, the color is ORANGE. Keeping it gives a final ORANGE.

The second record reads: start BLUE; input five, result ORANGE; input three, result ORANGE. Both worked records finish with input three. Their different final colors are consistent with the rule because the colors immediately preceding that input differ. The last input number alone does not select one final color here.

To separate the starting color from the intervening step, make a third record that starts BLUE and receives one followed by three. One sets BLUE; three keeps BLUE. This third record and the second record share the same starting color and final input. Their different middle results still explain their different endings.

Compare the entries just before the last step. In the second record, five has made the state ORANGE. In the third, one has left it BLUE. That is the information three uses. You do not need to call either record mistaken or invent an unstated action to reconcile them.

Check all ten state-and-input combinations

There are two possible starting colors for a single step and five permitted inputs. Listing each input once under BLUE and once under ORANGE gives ten combinations to inspect. This small complete list lets you check the rule directly rather than relying on one memorable example.

With BLUE present before the step, input one gives BLUE, two gives BLUE and three gives BLUE. Input four gives ORANGE and five gives ORANGE. The three BLUE results have different explanations: one and two set BLUE, while three keeps the BLUE that was already present.

With ORANGE present before the step, input one gives BLUE and two gives BLUE. Input three gives ORANGE, four gives ORANGE and five gives ORANGE. Here three keeps ORANGE, whereas four and five set it. Write those reasons beside the entries if the matching colors make the cases seem interchangeable.

Read the two entries for input three together. BLUE before three gives BLUE afterward. ORANGE before three gives ORANGE afterward. Those two entries establish the exact dependence being examined. Reporting only one of them would leave out a permitted starting state.

Now compare the two entries for input one. Both finish BLUE despite different preceding colors. The same is true for input two. Four and five similarly finish ORANGE from either permitted color. This contrast comes from the complete ten-entry list, without assuming a behavior beyond the written rule.

A check that uses only input one would not reveal whether someone has copied the instruction for three correctly. Both BLUE and ORANGE starts would finish BLUE at one. Include both starting colors at three when checking a transcription of the complete worksheet rule.

Suppose a copied table says that three always produces BLUE. It agrees with the correct BLUE-to-BLUE entry but disagrees with the ORANGE-to-ORANGE entry. The ORANGE starting case locates the mistake precisely. Changing that entry to keep ORANGE repairs the copied table's stated rule; it demonstrates nothing about an actual product.

Keep the previous indicator state beside each input

For the previous indicator state, write the color immediately before the current input. A useful record has four labelled spaces: step number, color before, input, and color after. Complete the color-after space using the rule, then carry that result into the next line's color-before space.

Try this longer, original record: start BLUE, then use inputs one, five and three. The first result is BLUE. The second is ORANGE. The third remains ORANGE. At the final step, previous means the ORANGE produced by five, not the BLUE written at the beginning of the page.

Keep the initial entry visible even though it is not always the value carried into the final step. It tells a reader where the record began. Each later line tells the reader which state was available for that particular input. These entries answer different questions within the same trace.

If a record gives only a final three with no preceding color, leave the final color undetermined. The complete rule permits BLUE or ORANGE, depending on the missing entry. Do not fill the gap by choosing the color seen in another record or by treating a blank as BLUE.

If the preceding color is known, the result at three is specific. A line saying color before ORANGE, input three, color after BLUE conflicts with the worksheet rule. Check that line against the ORANGE-and-three entry in the complete list. Here the record contains enough information to identify the discrepancy.

Inspect an earlier questionable line before relying on later ones. If a record wrongly changes ORANGE to BLUE at three and then correctly keeps BLUE at another three, the later line can follow its own recorded starting state while the complete history remains inconsistent with the original rule. Mark where the first mismatch occurs.

For a separate short check, start BLUE and use three three times. The result remains BLUE after each step. Starting ORANGE and using the same three inputs leaves ORANGE after each. Repetition of the middle input does not introduce a new color-setting instruction into either of these two explicit traces.

Keep a fresh record separate from a continued record

You may choose either starting color for a new worksheet record. State that choice before tracing its first input. Choosing a fresh BLUE start between two records does not mean that input three sets BLUE. It means that a new record was started with a separately declared initial color.

For example, a completed record may finish ORANGE after five and three. If the next independent record starts BLUE and receives three, it finishes BLUE. Keep the new starting entry visible. Otherwise, a reader could mistake the two independent records for a single continued history with an unexplained color change.

This distinction needs no instruction for resetting equipment. You are naming the beginning of an invented paper record. It has no power button, memory storage feature or physical control to operate. Keep the written starting choice within the exercise rather than presenting it as a repair action elsewhere.

Use related state guides within their own limits

The DR-40X loop playback guide separates suspending a loop, retaining its boundaries and clearing them under the applicable manual. Its controls remain specific to that recorder. Here, keep the previous color beside the input instead of assuming that every step replaces it with a newly chosen color.

The La Crosse changing-display guide identifies the selected view before treating changed digits as a stored-time fault. Its clock modes do not belong to this worksheet. The relevant reading habit is to name the missing context: here, the color immediately before input three.

Both links concern actual equipment with its own documentation. The paper rule supplies no control sequence or diagnosis for either device. Keep its complete definition on the page so another reader can check the invented records without borrowing a button meaning or a product feature.

Finish with the rule and the two different endings

For your final explanation, give the input and preceding color together. “Three leaves BLUE because BLUE was already present” and “three leaves ORANGE because ORANGE was already present” are both complete statements under this rule. That instruction explicitly uses both the input and the preceding color.

Return to the first two records. ORANGE followed by inputs one and three ends BLUE. BLUE followed by five and three ends ORANGE. All four steps match entries in the complete ten-combination list. The differing endings need no extra operation or change to the declared rule.

Keep the ingredient shopping references separate from that conclusion. No color in these records establishes a powder's condition, activity or suitability. A checked paper trace completes only the task defined by its two colors, five inputs and written transition rule.

Paper indicator memory is the reason to retain the state immediately before the middle input. When checking this worksheet, use both that state and the input number. A final three can correctly leave either color; the preceding line tells you which result the particular record requires.