October 27

Less with more

We have two jugs, 4 and 3 gallons, and plenty of water: how can one obtain 1 gallon of water?

Same question if the jugs volumes are 5 and 2? 7 and 2? 5 and 3? 

What about 6 and 3? 6 and 2?

Paying your dues

In Oddland, they have coins of 3 and 7 cents only. Can one pay 8 cents in exact change? 9? 10? 11 cents? 

In Evenland, they have coins of 2 and 6 cents. Can one pay 8 cents? 11?

Criss-cross

In the game of "cross-cross" on needs to add straight segments connecting points. No intersections allowed! Whoever makes the last possible move, wins. Who would be that?

Pascal triangle

robotic adventures continue: we are counting the numbers of ways to get from start to each of the crossings. 

These numbers have a name: Binomial coefficients, and are typically arranged as the

Pascal triangle:

start

1   1

1   2   1

1   3   3   1

1   4   6   4   1

...

SET

we will try the real game

As an experiment, we'll try the constant width (a.k.a. Reuleaux) rollers...