Group 1 (6-7 year olds)
Continue the pattern:
Move
2 matchsticks to get 5 equal squares.
| Group 2 ( 9-10 year olds)
- Is it possible to put 5 checkers in such a way that each checker touches 3 others?
- Alcuin's "grain problem" : A head of household has 20 servants. He ordered them to be given 20 sacks of grain as follows: men will receive 3 sacks, women 2 sacks, and the children, half of a sack. How many men, women and children are there, if there is at least one of each?
- There are ten gnomes caught by a dragon. He has given the gnomes a chance of survival. Here is the offer: The dragon lines the gnomes up in a single row ( as shown). The dragon has a large bag full of black hats and white hats. The dragon randomly reaches into his bag and places a hat on each of the gnomes. The dragon asks the gnome, "What color is your hat?" If the gnome answers correctly, he lives and gets freed from the dungeon. If he does not, he dies. He continues up the line in this progression. However, before placing the hats on the gnomes, he allows the gnomes to meet as a group and discuss a strategy to save as many of the gnomes as possible. Imagine that you are one of these gnomes. What strategy would you develop? How many gnomes can you guarantee to save? (You must ONLY say "white" or "black”)
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