Solutions

Tic-Tac-Toe

How many symbols can you arrange in a Tic-Tac-Toe square without having three symbols in a row. (Accord­ing to the rules of Tic-Tac-Toe, but only one type of symbol)

6

Integer Sequences

Determ­ine the next number that logic­ally contin­ues the sequence:

6, 8, 12, 20, 36, …

68

xn+1 = 2(xn – 2)

Clock face

How do you divide the face of a clock into three parts using three straight lines so that the sums of the numbers in each part are equal?

Two Villages

You are at a fork in the road. Unfor­tu­nately, the signpost has been blown away. You know only that one path leads to a village of patho­lo­gic­al liars, and the other to one of vehement truth tellers. At the fork there is a person from one of the villages. What one question can you ask the person to tell you which road leads to which village?

On which path is the village you come from?

The person will always point the way to the village of truth. If they are from that village, they will always tell the truth, and there­fore point there. If they are from the other village, they must lie, and there­fore also point to the path of truth.

Nine Dots

Connect all nine dots with four straight lines without lifting your imagin­ary pen of the imagin­ary paper.

Shriv­el­ing Melons

A truck is trans­port­ing melons. At the start of their journey, the melons weigh one ton. The water content is 99%. Over the course of the trip, the melons lose water, ending up at 98% water contents. What does the load now weigh?

The melons now weigh 500kg.

The propor­tion of dry mass doubles from one to two percent. But since the absolute dry mass is constant, the total mass in the end must to be half of the mass in the beginning. 

The Hunting Dog

A hunter walks 2km from his lookout to his home at a constant speed. His overzeal­ous dog runs ahead and arrives before him. From there, the hunting dog immedi­ately returns to the hunter. When he reaches the hunter he turns back and runs home. This goes on, back and forth, until the hunter arrives home. What distance has the dog run in total if he moves at thrice the speed of the hunter?

The dog has run 6km.

As both creatures spend the same time in motion, and the dog has thrice the speed, the dog covers three times as much distance as the hunter. 3 times 2km are 6km.

Trapped Bees

There are ten bees are trapped under each of two cheese domes. In dome A all the bees are sitting on the ground. All the bees in dome b are flying about. Which cloche has a larger mass when weighed. 

Both scales show the same mass.