Rounding Windows Game

How to Play Rounding Windows

Construct the complete interval of real values that round to the displayed target at the stated step. Enter the exact lower and upper bounds, then choose whether each endpoint is included or excluded. The number line shows your proposed window when both bounds are within its view. Check window verifies the bounds and the endpoint rules together.

This game uses rounding to the nearest step with exact halves rounded away from zero. The convention is stated in every puzzle because rounding systems can use different tie rules. Halfway between two multiples, choose the multiple with greater absolute value. The two window boundaries lie exactly half a step below and above the target; whether they belong depends on how those exact ties round.

Enter decimals with at most three places, using a minus sign for negative values. The game parses them as exact scaled integers instead of comparing binary floating-point approximations. Equivalent decimal spellings, such as 5 and 5.000, represent the same bound. The answer is a full real interval, even when an Easy puzzle uses a whole-number rounding step.

Worked Positive, Negative and Zero Windows

To round to 60 at the nearest-ten step, the midpoint bounds are 55 and 65. The exact value 55 rounds away from zero to 60, so it belongs. The exact value 65 rounds away from zero to 70, so it does not. The complete interval is [55, 65): the square bracket includes 55 and the curved bracket excludes 65.

For a target of −60 at the same step, the interval is (−65, −55]. The exact value −65 rounds away from zero to −70 and is excluded, while −55 rounds to −60 and is included. For a target of zero, both ties are excluded: at step 10, the complete window is (−5, 5), because −5 rounds to −10 and 5 rounds to 10.

At the nearest-hundredth step, a target of 0.27 has boundaries 0.265 and 0.275. The interval is [0.265, 0.275). A tiny error in either bound would omit valid values or include values that round elsewhere. This is why the game asks for exact midpoint boundaries rather than an approximation or a selection of a few sample values.

Rounding Levels, Controls and Saved Answers

Easy uses nearest-ten and nearest-hundred tasks with positive targets. Normal introduces smaller steps, decimal targets and zero. Hard can use negative targets and nearest-hundredth steps. All levels apply the same explicit away-from-zero tie rule. Choosing a different conventional rounding rule is not an accepted answer to the stated puzzle.

Type in the bound fields and choose Include or Exclude from each endpoint menu. Enter submits the form. A hint gives the half-step distance and reminds you how to test a tie. Undo restores the preceding endpoint-menu change and its saved bounds; typing alone does not add an Undo step. Neither hint nor Undo substitutes a solved result without your input.

Daily and Practice answers save separately by level, including incomplete fields. Daily tasks change at midnight UTC. Wrong checks reduce the possible score by five points and hints by fifteen, with a minimum completed score of ten. Hints and Undo mark assistance, so their rounds do not replace an unaided best. A completed puzzle is counted once. Browser saving is local, and the controls still work when saving is unavailable.

Frequently Asked Questions

Which rule is used for exact halves?

Exact halves round away from zero, as stated in every puzzle.

Is zero’s rounding window closed?

No. Under this rule, both half-step endpoints round away from zero and are excluded.

Are the bounds rounded approximations?

No. They must be the exact midpoint bounds; decimal inputs with up to three places are parsed exactly.