Place Value Exchange Game

How to Play Place Value Exchange

Match the displayed piece count in every place while keeping the total number unchanged. The bank shows your current pieces and the goal for ones, tens, hundreds and any larger places included in the selected level. A check mark appears beside a matching row. The round finishes when every row has exactly the required count.

Bundle exchanges ten pieces in a smaller place for one piece in the next place: ten ones become one ten, ten tens become one hundred, and so on. Split performs the reverse exchange. Both trades preserve value. You may bundle only when at least ten smaller pieces are available, and split only when the larger place contains a piece to exchange.

The board allows at most 200 pieces in any single place. A trade that would exceed that limit is unavailable. The total value stays visible throughout, so this task is about equivalent representations rather than changing the answer. Easy and Normal use the standard representation with fewer than ten pieces in each place. Hard can request an intentionally unbundled representation, requiring attention to the exact goal counts.

Worked Example: Regrouping 342

The standard representation of 342 is three hundreds, four tens and two ones. An equivalent bank may contain two hundreds, thirteen tens and twelve ones: 2 × 100 + 13 × 10 + 12 × 1 = 342. Bundle ten ones into one ten to get two hundreds, fourteen tens and two ones. Then bundle ten tens into one hundred, producing the standard representation.

The reverse trade explains borrowing in subtraction. Splitting one hundred from three hundreds gives two hundreds and ten additional tens. Splitting one of those tens gives ten additional ones. These exchanges change how the number is represented while preserving its total. They do not add a new hundred or remove value from the bank.

A nonstandard goal can be equally valid. For example, 342 can be represented by three hundreds, three tens and twelve ones. Its value is still 300 + 30 + 12 = 342. When a Hard puzzle asks for a particular unbundled row, merely forming the usual digits is not a complete answer. Match each displayed goal, including any row that deliberately contains ten or more pieces.

Base-Ten Practice, Levels and Progress

Easy uses three places, Normal four, and Hard five. The larger places extend through thousands and ten thousands. The named trade rows make the relationship between adjacent places explicit, so you can work systematically from a lower place upward or split a higher place when smaller pieces are needed. All mathematical checks use exact whole-number values.

Each Bundle and Split button works by touch, Tab, Enter or Space; no dragging is required. The buttons are disabled when the bank lacks the required pieces or a place limit would be exceeded. Undo restores the preceding bank and marks assistance. A hint suggests one conserving trade toward the displayed goal rather than changing the bank automatically.

Daily mode changes at midnight UTC and repeats the same task for a given level and date. Practice offers another bank through New puzzle. Current counts and completed results save locally when possible. Wrong choices reduce the possible score by five points, and hints by fifteen, with a ten-point floor on completion. Hints and Undo mark assistance; assisted rounds do not replace an unaided best, and the same completed puzzle is recorded only once.

Frequently Asked Questions

Do exchanges change the number?

No. Ten units in a smaller place have the same value as one unit in the next place.

Can a goal contain more than nine pieces?

Yes. Hard can request a specified nonstandard representation. Match each displayed goal count.

What is the piece limit?

Each place can hold at most 200 pieces on this board.