Dice Problems — Prelims Strategy

Prelims Strategy

For a labelled-view question, write confirmed adjacencies before assigning opposites. Count distinct neighbours, not the number of views in which a label appears. Repeated evidence about the same neighbour does not add a new constraint. If a question gives ordered top, front and right positions, preserve that order and distinguish rotations from mirror arrangements.

For rolls, define towards the observer and right on the page, then update the six-position table after every move. Check that opposite pairs remain opposite. The face towards which the die rolls becomes the bottom, which prevents a common top-face reversal. Do not combine separate one-roll answers without carrying the changed orientation forward.

For probability, confirm fairness and independence, identify whether order distinguishes outcomes, and count overlaps once. Two dice give 36 ordered outcomes under the standard assumptions. At least one invites a union count or a complement; both invites an intersection. Reduce the fraction only after the event has been correctly identified, and check that the final value lies between zero and one.