april 27

A dragon eats for breakfast an apple and a boar. A unicorn eats for breakfast 2 apples. Some number of unicorns and dragons met for breakfast and ate three boars and seven apples. How many dragons and unicorns met?

Same question for five boars and eight apples. OK, nine apples. For which numbers this puzzle has an answer?

Pete goes from Champaign to Savoy (6 miles), making 2 miles per hour. Slow Joe goes from Savoy to Champaign, on the same road, making 1 mile per hour. How far from Champaign will they meet?

Graph paper and rulers. Coordinate axes. Place points. Are the three points on one line?

Straight line on graph paper: can it cross first two horizontal then two vertical bars? Write down sequences you see (VHHV, as an example).

april 20

Pascal triangle mod 2 (did not work, return later)

More Chinese reminders

Game with stickers on forehead: each reports how many blue/red stickers they see; define their own color. Two stickers?

Graph paper and rulers. Coordinate axes.
Place points. Are the three points on one line?

april 13

Add numbers separated by two. Is the result always even? Add three numbers separated by two... What now?

More Chinese reminders

Game with stickers on forehead: each reports how many blue/red stickers they see; define their own color. Two stickers?

Graph paper and rulers. Coordinate axes.
Place points. Are the three points on one line?

Digital straight line: draw line; see how the horizontal/vertical bars are intersected. Is there a pattern?

Unknot an unknot

copper tube experiment

4.6

Add neighboring numbers: why the result is always odd?
Add three neighboring numbers: what it is divisible by?
What about four neighboring numbers?

Pascal triangle mod 2

Post-it puzzle: Alice, Bob and Claire see the others' numbers, not theirs. Alice sees 3, Bob 3, Claire 2. What numbers each has?

Same with kids

Hedgehog wants to bring an apple to the porcupine, and return back

SET

Disentangle 

march 9

Chinese reminder theorem:

Some number of apples (stones) on the table (cover them).
If divided between 2 people, 1 is left, if between 3 people, none left.
If divided between 2 people, 1 is left, if between 3 people, also 2 left...
If divided between 2, none left, if between 3, 2 left. (8? what about 2?)

Right triangles. Define, look for right triangles. Split a given triangle into 2 right ones. 3? 4?

Carrying stuff around. Wolf-Goat-Cabbage problem.

SET

Round sticks balancing

February 16

Robots: wrote letter S (E4 N3 W4 N3 E4, or like); digit 7...

Navigated two robots in a maze past each other.

Word problems: Crocodiles got a package with fresh nasty boys. If each croc tries to get 2 boys for lunch, one croc will get none. If each croc gets just one boy, there will be one boy left. How many crocs and boys were there?

January 26

Program robots to write words.

Symmetry again - this time with several axes

Goat problem: where the grass was eaten?

Gallery guards: how may ways to place them?

SET!