TRY IT · FLIP EITHER SWITCH

→
XOR answer · y1Different → on

These four examples are the entire problem.

TRY IT · MOVE THE LINE

3 / 4 correct
XOR targets and a movable boundaryTwo target ones are on opposite corners. Shading predicts one. Wrong predictions have a dashed ring.

● target 1 ○ target 0 predicts 1

Keep the 1s inside.
Keep the 0s outside.

The (1, 1) example is on the wrong side.

The rulescore = w₁x₁ + w₂x₂ + bWeights w₁, w₂ tilt the line; bias b moves it. Score ≥ 0 → 1. Otherwise → 0.

TRY IT · FOLLOW ONE EXAMPLE

4 / 4 correct

h₁, h₂ = hidden answers · ŷ = prediction

Two cutoffs create a bandThe shaded band predicts one for the two different-input examples and zero for the same-input examples.

predicts 1 Dashed ring = wrong

ADD THE INPUTS1 + 0 = 1
↙↘
AT LEAST ONE?h₁ = step(sum − 0.5)step(1 − 0.5)1yes
BOTH?h₂ = step(sum − 1.5)step(1 − 1.5)0no
↘↙
FIRST YES, SECOND NOŷ = step(h₁ − h₂ − 0.5)step(1 − 0 − 0.5)1Correct · target 1

One switch on falls between the cutoffs. Both on passes both checks, so the second cancels the first.

Drag a cutoff to break the rule. Or turn the hidden steps off—the final yes/no step stays on.