101 Z · 2026-10-21

101 Z: The Numbers Were Sorted, but the Cards Had Changed Order

Sort four labelled cards and inspect what happens to equal values. A second instruction makes preserving their original order part of the puzzle.

Four cards, two kinds of information

Place four handmade cards in this order: 3A, 1B, 3C, 2D. The number is the value; the letter identifies the physical card. In the 101 Z sorting puzzle, begin with just one instruction: arrange the values from smallest to largest.

One player produces 1B, 2D, 3A, 3C. Another produces 1B, 2D, 3C, 3A. Both have values 1, 2, 3, 3, so both satisfy that first instruction.

The letters allow a closer question. In the original row, 3A came before 3C. The first answer preserves that relationship, while the second reverses it. The number-only instruction did not specify which relationship to keep.

Add an order-preservation rule

Now add a second instruction: when values tie, preserve their order from the original row. Under this fuller rule, only 1B, 2D, 3A, 3C works. The extra condition changes which answers qualify.

Try building the row from left to right. Put 3A down, insert 1B before it, place 3C after the existing three, then insert 2D between 1B and 3A. Each step leaves equal-valued cards in their original relative order.

If you place the new 3C before 3A instead, the numbers still look sorted at that moment. The later arrival has crossed its equal-valued neighbour. This is the exact move that breaks the added order-preservation condition.

The exercise has a practical cousin in a reading list. Imagine sorting articles by game category while retaining the date order already present within each category. Equal categories need a defined treatment if the older ordering matters.

Letters identify; they do not rank

Do not use the letters as a hidden alphabetical tie-break. They identify the cards here. To see the difference, change the original labels to 3Z, 1B, 3A, 2D: preserving the old order keeps 3Z before 3A.

Ask a partner to verify the finished row in two passes. First check that values never decrease. Then check the original order of equal values. A single glance at the increasing numbers checks only the first condition.

The 101 Z puzzle ends with a precise distinction: sorted values and preserved tie order are separate properties. Naming both lets two people agree on what a correct arrangement must retain.

101 Z: The Numbers Were Sorted, but the Cards Had Changed Order

Four cards, two kinds of information

Add an order-preservation rule

Letters identify; they do not rank

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