Keep a total and split it — change one number while the total stays fixed

The four cards on the left are input cards. "Event budget" on the right is a result card showing their total. The small lock (🔒) at its bottom left means the total is fixed at $10,000.

Changing Food and drinks to 3,700 turns Venue, Prizes and Contingency into 3,600, 1,800 and 900. The cards that were adjusted flash a ring around their edge for a moment, and a notice at the top of the screen says how many cards were adjusted to keep the total. Food and drinks keeps the 3,700 that was typed.

Fixing the total

The total is fixed on a result card, which shows the sum of the numbers connected to it. A board like Board 1 can be built this way:

1. Put each number to split on its own input card.
2. Selecting an input card shows a ○ on its right edge. Dragging the ○ to an empty spot and letting go opens a list of cards that can be made there.
3. Pressing "Add result" in the list creates a result card connected to that input card.
4. Dragging the ○ of each of the other input cards onto the result card connects them too.
5. With the result card selected, opening ⋯ at its top right and pressing "Keep this total" fixes the total.

The total at that moment becomes the fixed value. The lock appears at the bottom left of the result card, and the menu item changes to "Stop keeping this total".

"Keep this total" appears in the ⋯ menu only when at least two input cards are connected to the result card. Input cards connected through a calculation card count too.

Changing the fixed value

A result card has no field for typing the fixed value. To change it, the total is unfixed first:

1. Pressing "Stop keeping this total" in the result card's ⋯ menu removes the lock.
2. Changing an input card now changes the total, and no other card moves.
3. Once the total is the value wanted, pressing "Keep this total" again fixes that total instead.

How a change is spread over the other cards

While the total is fixed, the result card's ⋯ menu shows four buttons for the way a change is spread: "By ratio", "Equally", "By weight" and "Top down". The selected one is highlighted; "By ratio" is the default.

The results below come from changing Food and drinks on Board 1. In every mode, setting Food and drinks back to 3,000 returns the other three cards to 4,000, 2,000 and 1,000.

By ratio

The change is shared in proportion to the other cards' current numbers. With Food and drinks at 3,700, what is left for the other three drops from 7,000 to 6,300. All three shrink by the same factor, to 9/10 of what they were, giving 3,600, 1,800 and 900.

Equally

With Food and drinks back at 3,000, pressing "Equally" in the ⋯ menu and then setting Food and drinks to 3,600 splits the extra 600 equally: each of the three cards drops by 200. Venue becomes 3,800, Prizes 1,800 and Contingency 800.

Top down

With Food and drinks back at 3,000, pressing "Top down" puts the numbers ① to ④ at the bottom right of the input cards. They are the order of adjustment: the higher a card sits on the board, the earlier it comes, and of two cards at the same height the one on the left comes first. The order of connecting and the card numbers play no part. Moving a card renumbers them.

Setting Food and drinks to 3,600 then changes only Venue, to 3,400. Leaving out the card that was changed, Venue is the top card, and it takes the whole difference. The cards further down move only once the first one has reached 0 (when reducing) or its upper limit (when increasing).

By weight

With "By weight" selected, the ⋯ menu of each connected input card shows "Share weight", which − and ＋ change; every card starts at 1. The difference is shared in proportion to the weights, so with Venue at weight 2, Venue moves twice as much as each of the others.

Cards that stay put

Pressing "Don't move this value" in an input card's ⋯ menu takes that card out of the adjustment and puts a lock at its bottom left. The same item then reads "Allow this value to move", which undoes it.

Only the input cards other than the one that was changed and the ones set to "Don't move this value" are adjusted. In no mode is a card adjusted below 0.

When a calculation card sits between the result card and the input cards, the total is still kept, but the ⋯ menu shows neither the spreading buttons nor "Split in whole numbers".

Upper and lower limits, and the order

When an input card is connected to a result card that keeps its total, the input card's ⋯ menu has "Set an upper / lower limit". Pressing it shows the fields "Min" and "Max" under the number. Adjustments made to keep the total never push the card outside that range. A number typed into the card by hand is taken as it is, even outside the range.

Board 2 splits the same budget "Top down". Venue has both Min and Max set to 4,000, so adjustments never move it. Food and drinks may range from 2,500 to 3,500 and Prizes from 1,500 to 2,500. Contingency has no limits.

Setting Contingency to 1,500 brings Food and drinks down to 2,500. The missing 500 is looked for from ① down; Venue at ① cannot move, so it comes out of Food and drinks at ②.

Setting Contingency to 2,000 next finds Food and drinks already at its Min, so Prizes at ③ goes down to 1,500.

When the total cannot be kept

Setting Contingency on Board 2 to 2,500 next leaves no card that can go down, so the total is not kept. A notice at the top of the screen says the limits were reached and the total could not be held. The other cards stay as they are, and the result card shows a total of $10,500.

The fixed value is still $10,000 all the while. Setting Contingency back to 1,000 makes the 1,000 needed to get back to $10,000 go in from ① down: Food and drinks rises to its Max of 3,500, and Prizes stays at 1,500. Contingency is back at its starting value, but Food and drinks and Prizes do not return to their starting 3,000 and 2,000, because a kept total is always adjusted from the numbers as they are now.

The notice that the total could not be kept appears in cases like these. In each, the result card shows the total as it then is.

• the cards to be adjusted have reached their limits;
• all the other cards are set to "Don't move this value";
• a card would have to go below 0 (for example after a large change with "Equally").

Splitting in whole numbers, or by the D'Hondt method

For things that cannot be split into fractions, such as seats or people, the total can be split in whole numbers. Board 3 shares out the 20 seats of a new office floor among four departments in proportion to their head count. The four cards on the left are the exact shares: Sales has 46 of the 100 people, so 9.2 seats. The result card "Seats" keeps its total at 20.

Pressing "Split in whole numbers" in the ⋯ menu of "Seats" makes all four cards whole numbers while the total stays 20: from Sales down, 9, 7, 2 and 2. Dropping the fractions gives 9, 6, 2 and 1, which is 18, so the remaining 2 seats go to the largest fractions: Engineering (0.8) and Planning (0.6). This is the largest remainder method.

After that, the ⋯ menu shows "Stop splitting in whole numbers" and "Use D'Hondt method". Pressing "Use D'Hondt method" gives 10, 7, 2 and 1. The same place then reads "Back to largest remainder", which returns the cards to 9, 7, 2 and 2.

Neither button rounds the whole numbers on screen again. The board remembers the 9.2, 6.8, 2.4 and 1.6 from before "Split in whole numbers" was first pressed, and every switch splits those again. So switching back and forth compares the two methods on the same starting numbers.

Typing a number into a card while whole numbers are on rounds a fraction to a whole number and adjusts the other cards in whole numbers. Typing 2.6 into Admin, for example, gives 3, and Sales drops to 8. Once a number has been typed, the first 9.2, 6.8, 2.4 and 1.6 are no longer used: "Use D'Hondt method" then splits the current 8, 7, 3 and 2 again, which in this example changes nothing.

Pressing "Stop splitting in whole numbers" leaves the cards at their whole numbers; they do not go back to the fractions.

Whole numbers work only when the fixed total is a whole number (after taking away any cards set to "Don't move this value"). Otherwise no card changes, and a notice says the total cannot be held in whole numbers. On money cards, the same option splits a budget in whole dollars.

How this differs from building the split with min()

A split by caps and priorities can also be built with formulas: starting from the total, each item gets min(what is left, its cap), and what remains passes to the next item. The two approaches differ like this:

The formula board splits again from the start, by the same rule, every time the total changes. The result card takes care of the rest of the split when the total is decided and the items are changed one at a time by hand. That is why, on Board 2, setting Contingency back to 1,000 did not bring back the starting split.

When it does not work

• "Keep this total" is not in the ⋯ menu — it is only on result cards, and only when at least two input cards are connected to the result card.
• The spreading buttons or "Split in whole numbers" are missing — the total is not fixed, or a calculation card sits between the result card and the input cards.
• An input card has no "Set an upper / lower limit" — it is not connected to a result card that keeps its total.
• Changing a number moves no other card — without a lock on the result card, the total is not fixed. With the lock and a notice, the limits or "Don't move this value" have left no card that can move.
• "Top down" starts with an unexpected card — the order comes from the positions on the board; the ① ② at the bottom right of the input cards show it.
• Cards show long decimals — "By ratio" and "Equally" leave fractions when the numbers do not divide evenly. "Split in whole numbers" keeps them whole.
• Switching methods does not give the first split — after a number is typed into a card while whole numbers are on, splits start from the current numbers.

Read next — Save, share and embed Where boards are saved, how to send one as a link or an image, and how to keep numbers you changed on an article's board.

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