The applets here are designed to explore school mathematics concepts and can be successfully executed on either a standard computer screen or on the interactive whiteboard.
Cups are arranged in a row and randomly placed either upright or upside-down. The only move that is permitted is to selected any two neighbouring cups and rotate them both. By repeated application of this simple move is it possible to end up with all the cups upright? The challenge is to discover and give a convincing description of a simple rule for predicting in advance whether or not this puzzle can be solved, and if the puzzle can be solved to describe a strategy of moves for solving it.
This is a game involving one player and three lifts. Two of the lifts are going down and one is going up, but the direction of each lift is decided by the program and not revealed to the player. The aim of the game is for the player to guess which lift is going up. Stage 1: the player selects one of the 3 lifts and the program responds by revealing one of the other two lifts which is going down. (At least one, and possibly both, of the other two lifts is going down. If both are going down the one revealed by the program is selected at random.) The direction of the other two lifts is not yet revealed. Stage 2: the player now selects one of the two lifts whose direction is not yet revealed and the program responds by finally revealing which lift is going up. If the lift selected at stage 2 is the one going up then the player wins the game, else they lose. The question is what is the best strategy for the player to adopt in order to maximise the chance of winning? To be specific, at stage 2 should the player always select the same lift they selected at stage 1 (i.e. stick with their first choice), or should they always select the lift not selected at stage 1 (i.e. switch their choice to the other unrevealed lift), or does it not make any difference to the chances of winning whether they stick or switch? This applet enables the game to be played repeatedly and the applet displays both the percentage of times the player wins (i.e. successfully selects the lift going up) when they stick with their first choice and when they switch their choice of lift.