Remainder Race Game

How to Play Remainder Race

Reach the exact finish value by adding the remainders from verified divisions. The upcoming dividends are shown in order so you can plan ahead. For the current dividend, choose an unused divisor card, enter the quotient and remainder, then select Check division. A correct division advances the round and adds its remainder to your progress.

Use Euclidean division: dividend = divisor × quotient + remainder, with a nonnegative quotient and a remainder at least zero but smaller than the divisor. Every divisor card can be used only once in a puzzle. A remainder of zero is a valid result and uses a round without adding distance. The game rejects a false division or a remainder that would pass the exact finish value.

You may reach the target before the last allowed round. Otherwise, keep choosing divisors for the next displayed dividend until the finish is exact. If the round limit is reached without finishing, use Undo or Reset race to try another plan for the same puzzle. No cars, reaction timing or unrelated arcade actions determine progress; the calculations and divisor choices do.

Worked Example: Divisors Change the Remainder

Take a dividend of 29. Dividing by 5 gives quotient 5 and remainder 4 because 29 = 5 × 5 + 4. Dividing by 6 also gives remainder 5: 29 = 6 × 4 + 5. Dividing by 7 gives remainder 1: 29 = 7 × 4 + 1. Those different remainders can produce very different progress toward a fixed finish value.

Suppose two dividends are 29 and 22, the finish value is 5, and divisor cards 5 and 7 are available. Use 5 for the first dividend to add remainder 4, then 7 for the second to add remainder 1: 22 = 7 × 3 + 1. The remainder total is 4 + 1 = 5. A different first choice could leave too much or too little progress for the remaining cards.

The remainder limit matters. Writing 29 = 5 × 4 + 9 is a true arithmetic equality, but it is not the required division result because 9 is not smaller than 5. Increase the quotient and reduce the remainder until it lies in the allowed range. Review Verified divisions to inspect every accepted equality and its contribution to the exact finish.

Levels, Planning and Saved Races

Easy uses smaller dividends, six divisor cards and at most three rounds. Normal provides eight cards and four rounds with larger dividends. Hard has ten cards and five rounds. Each generated puzzle includes a verified plan, and any other legal sequence with the correct total is accepted. The visible future dividends help make this a planning challenge instead of a sequence of blind guesses.

Choose cards by touch or keyboard. Enter moves from a division field to Check division through the usual form controls. Undo restores the previous round or card selection and marks assistance. Reset race clears progress for the same puzzle and also marks assistance. A hint searches from your current progress; it either supplies a valid next division or explains that Undo is needed.

Daily and Practice sessions save independently by level, including selected cards and unfinished quotient/remainder entries. A completed puzzle is counted once in local records and the practice calendar. Wrong checks reduce the score by five points and hints by fifteen, with a minimum completed score of ten. Assisted rounds do not replace an unaided best. There is no timer, and play remains available when browser saving is blocked.

Frequently Asked Questions

How small must a remainder be?

It must be at least zero and strictly smaller than the positive divisor.

Can I reuse a divisor card?

No. Every displayed divisor card may be used once in a puzzle.

Does a correct division always advance safely?

Its remainder must also keep your progress at or below the exact finish value. A correct division that overshoots is rejected.