Vector Countdown

Combine six tiles, column vectors and scalars, to make a vector as close as you can to the target before the clock runs out

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TARGET?
targetfirst vectorsecond vectorresultbest solution

Score

Round 1
How to play

Choose six tiles one at a time from the Vector pile (column vectors such as ) and the Scalar pile (numbers such as , and at Hard also negative scalars and ), or deal six. The target vector stays hidden until you press Start the clock (or Reveal the target with no clock).

Tap a tile, an operation, then another tile. You can add or subtract two vectors (add or subtract the components), multiply a vector by a scalar (multiply each component), divide a vector by a scalar when each component divides exactly, and add, subtract or multiply two scalars. You can’t multiply two vectors together. Every vector you make must have integer components, no step may give 0 or the zero vector, and each tile can be used once.

The grid draws each step head to tail: for , starts where ends, and the result goes from the start of to the end of . Tap a line of your working to draw that step again.

How close you are is the magnitude of the difference, , between the target and your vector : for example is from . The shaded circles round the target have radius and .

Show your working (on unless you turn it off): you type the result of each step before the new tile is made, a vector’s two components in the two boxes. After two tries you get a hint, after three you can ask to be shown.

Keys: 1–9 pick a tile, + - * / the operation, Backspace undoes, Enter declares.