Play Quads

The cards and the quad rule

Each card has a color, shape, and count. Quad-128 and Quad-256 also use a background color.

Color

blue, orange, purple, or green

Shape

square, triangle, circle, or heart

Count

1, 2, 3, or 4 symbols

Background

white, pale blue, pale orange, or pale green in the larger decks

A quad is four cards for which each attribute is all the same, all different, or two pairs. Apply the rule to background color as well when the deck has multiple backgrounds.

Quads Deck

Choose 16, 32, 64, 128, or 256 to see all cards in that deck. For decks of 32 or more, the lower half of the locations read left-to-right, top-to-bottom on the left side, and the upper half do the same on the right. The decks are nested: the cards in a smaller deck appear again in each larger deck.

Play

Choose a deck size and a deal size (the number of cards shown at once), then click New game. You can change these settings for another game. Suggested starting deal sizes:

• Quad-16One color · 6–7 face-up cards
• Quad-32Two colors · 7–8 face-up cards
• Quad-64Four colors · 8–10 face-up cards
• Quad-128Two backgrounds · 10–12 face-up cards
• Quad-256Four backgrounds · 14 face-up cards

1. Click four cards that you think make a quad, then click Check selected (4). Click a selected card again to deselect it.
2. If they make a quad, the four cards move to Found quads. The game deals replacement cards while cards remain in the deck. If they do not make a quad, try a different selection.
3. Click Hint to highlight a card that helps you find a quad. Click Add card to deal one more card when the deck has cards left.

End Game

Choose a deck size, then open End Game. The app secretly removes one card and plays ahead until no quads remain. Your task is to identify the hidden card from the cards left on the table.

1. For each relevant attribute—shape, count, color, and, in larger decks, background—look at the remaining cards. Set aside matching pairs or groups of four.
2. If one card remains for an attribute, the hidden card matches it. If three remain, choose the value that completes a group that is all the same, all different, or two pairs.
3. Use the attribute menus to describe the hidden card, then click Check guess. You may try again if the guess is incorrect. Click New game for another hidden card.

For a 64-card deck, the end typically leaves three or seven cards. With three cards, the hidden card completes their quad. The example below shows the seven-card method.

One Color Challenge

The 16 purple cards are split into two complementary groups of eight. Each grid shows one group face-up; its other eight cards show ℚ backs. Solve the two grids separately.

1. Click four face-up cards that you think make a quad, then click that grid’s Check selected (4).
2. Keep finding different quads until the grid reports that you found them all. The cards remain visible after a quad is found. Use Clear selection to start a new choice.
3. Click New challenge to get two new groups.

Quad Quilting

1. Choose a Deck size and a Quilt size. Every card in the source deck is available. For example, choose a 64-card deck and a 4 × 4 quilt to arrange 16 of those cards. Quilt sizes larger than the source deck are unavailable.
2. Click Start quilting to empty the quilt and show the card pile. Scroll within the pile to see more cards. Drag a card into any cell, or click a card and then its destination. You may place cards in any order; placements are not checked while you work.
3. The cells outlined in orange define the basis: the cards in these cells determine the correct arrangement of the remaining cards. Your goal is to build a quilt whose cards follow the quad patterns determined by that basis. A smaller quilt must contain the cards determined by its basis, so an arbitrary selection of the same number of cards may not make a valid quilt.
4. To move a placed card, drag it to another cell, or click it and then its destination. If the destination already contains a card, the two cards swap. Placing a card from the pile onto an occupied cell returns the displaced card to the pile. Undo placement reverses the most recent placement, move, or swap.
5. Labels are hidden by default. Under Labels, choose Card values to show each placed card’s binary value, Location numbers to show each quilt position’s binary value (including empty positions), or No values to hide them.
6. For a hint, click a quilt cell and then Hint for selected cell. The selected cell is outlined in blue; three other cells containing placed cards are highlighted in purple. Those four positions should contain a quad in a correct quilt. A hint does not check whether the cards currently in those positions are correct. If no suitable trio of occupied cells is available, no hint is used. You have three hints per quilt. Selecting another cell or moving a card clears the hint highlights.
7. Once every quilt cell contains a card, click Check quilt. Green ✓ marks a card that matches the arrangement determined by your chosen basis; red × marks a card that does not. If the basis cards cannot define a valid quilt, the basis cells are marked with ! and the other cells are not graded. Revise the basis and check again.
8. Make corrections by moving, swapping, or replacing cards, then click Check quilt again. Start quilting starts a fresh quilt. Standard layout shows the original arrangement for the chosen quilt size and exits manual quilting. Either action, or changing the deck or quilt size, clears your work and resets the hint allowance.

Quad Packing

The entire deck automatically scales to fit the screen when you change the deck size or resize the window.

Use Show labels to display or hide binary labels, and choose Location or Card value in the label selector.

Choose a deck size and use Random subset to choose the face-up cards; the counters show the number of face-up cards and all quads contained in that subset. Quads may share cards.

Enter a size in Random subset and click Generate subset. Individual cards cannot be added or removed by clicking them. Choose a Partition, then click Select Phi Map. Pick a face-up card b in the pale purple region (B), then a face-down card a in the pale gold region (A). Dark gold rings show where every face-up card in B maps, including targets that are already face-up.

Click Apply Phi Map to move each face-up card x in B to x ⊕ a ⊕ b in A when its target is face-down. Compare the quad counts before and after. Undo φ-map reverses the last map; Clear cancels the current selection.