Boxes and beads
We have three boxes, whose contents we cannot see, and each of them contains two beads: in one there are two white beads, in another there are two black beads, and in the third there is a black and a white bead. Each box is labelled with a sticker, but each one of them has the wrong sticker. What is the smallest number of beads that we need to take out in order to know the exact contents of each box?
When you ask Mrs. Thomas the age of her children she replies that the youngest one is either Ana or Bill, but Ana is the oldest only if Carl isn’t the youngest. Can you conclude from this who is the oldest, and who is the youngest between the brothers?
Mr and Mrs. Holst and their two children are a normal family. But, if only two (only two - no more, no less) of the four stated claims are true, can you conclude what their names are and who is who in the family?
- John and Leena are related.
- Bjorn is older than John.
- Diana is younger than Bjorn.
- Diana is older than Leena.
Three men are standing in a line, one behind the other, so that the last one sees the two in front of him, and the one in the middle only sees the one in front of him, and the first one in line doesn’t see any of them. There are also caps included: three blue ones and two red ones. A cap is placed on each of their heads, and the rest are put on the side where none of the men can see them. The three of them all know how many caps there are and what colours they are but they do not know where they are. The last one in the line claims he cannot determine the colour of the cap on his head, thereafter the man in the middle claims the same thing. But the one standing at the front of the line, and cannot see the two of them, after hearing their answers, correctly concludes the colour of his cap. How and what colour is his cap?
One explorer decided to cross the desert, but he found out that for the crossing he would need 6 days, and one man by himself can only carry reserves for four days. What is the smallest number of people he needs to take with him in order to cross the desert?
Theo and Anna went to the forest to pick mushrooms. Since their mother forbade them to pick any unfamiliar mushrooms, they were only looking for boletuses and chantarelles. In total they picked 70 mushrooms. Can we calculate how many each of them picked, if we know that Anna had 4/9 of the total number of boletuses picked in her basket, and Theo had 3/5 of the total chantarelles picked in his basket.
This year, one fourth year high school class showed a great interest in learning foreign languages. From 30 students in the class, only 2 of them did not choose an extra foreign language. Of the remaining students, 14 of them chose Italian as an extra subject, and 22 chose Spanish. Can you conclude from this how many students chose two languages as an elective course?
An apple orchard was attacked by aphids and every single day there were two times more orchards affected than the day before. By the sixth day, the entire orchard was infected. In how many days was half of the orchard infected?
Yesterday, in class 4C, there were 4 times more students present in class than the number of students who stayed at home due to flu. One student came back to class today, so the number of students present in class was 5 times more than those absent. How many students are there in total in the class 4C?
Someone asked the farmer at the fair: - How many sheep do you have in your flock. He answered: - Today I bought 30 sheep and now there are three times more than there were before. How many sheep does the farmer have?
A group of researchers arrived at their destination, but before they hoisted their tents, they decided to send some scouts to check the grounds. The leader of the group selected two of them and sent them to the south. Even though both of them went in the direct of south, after each of them passed 100 metres, they were distanced 200 metres from one another. How is this possible?
Yesterday, Mrs. Mary brought eggs to sell at the market. The first customer immediately bought half of the eggs and half an egg, so she was left with only 50 eggs to sell. How many eggs did Mrs. Mary bring to the market if we know that none of the eggs were smashed?