Insert mathematical signs between digits 1,2,3,4,5,6,7,8,9 to make an expression that equals 100. The digits must remain in the same sequence. There are many different solutions, so try and figure out at least one!
(MartinShCol - 3.13) Insert mathematical signs between digits 1,2,3,4,5,6,7,8,9 to make an expression that equals 100. The digits must remain in the same sequence. There are many different solutions, so try and figure out at least one!
1+2+3+4+5+6+7+ 8*9
1 – 2 + (3+4)*5 + 6*7 + 8-9
1 + (2*3*4*5)/6 + 7 + 8*9
Sqrt (-1+2+3) + (4!*5) + 6 - 7 - 8 – 9
-1 + 2*3*4 + 5*6 + 7*8 – 9
Homework: Kids to try more options
(MC - 0 - 6) In a certain year there were exactly four fridays and exactly four mondays in Jan. On what day of the week did 20th Jan fall?
Answer: Sunday
Instructor Note: Show on board. What if the same held true for April (note there are 3 answers, and kids should come to that conclusion on their own)
How many pipes of 1 inch dia are required to carry same water as a pipe of 6 inch dia. Similarly for volume - height of scale model of Eiffel tower which is 1/1000 the weight
Answer: 36 and 1/10
Instructor Note: Ensure kids understand area and volume correspondence to length. Show with pipes or by cutting holes of that dia in paper and filling with layers of beads, or math copy squares. (AM: THIS PROBLEM DIDNT WORK WELL - LOOKED LIKE TOO MUCH MATH)
(Arjun contributed) There is a circular house with circular rooms and circular furniture. The man of the house is murdered. The mother says she was in the kitchen, the help says she was busy cleaning a room, and the child says he was quietly reading a book in a corner. Who murdered the man?
Answer: the child - there is no corner in the house
Homework: Actually, there might be corners in the house if any two rooms, or the room and house share a "wall". Interesting follow up discussion. Kids to enjoy patterns by taking any shape and filling it with circles, always drawing the largest circle they can in the remaining space.
(Shakuntala - 198) Two farmers set out to sell 30 oranges each, first for 3 a rupee, and second for 2 a rupee, hence garnering Rs 25 between them. Next day, they decided to sell for 5 for two rupees, but only got Rs 24 in all - where did one rupee go?
Followup: A train travels at 40 kmph on its way up the mountain and 60 kmph on its way down. What is the average speed? What if the train traveled at 40 kmph for 40 km, and 60 kmph for 60 km?
Instructor Note: Idea is for kids to understand that averages work differently when denominators are changing.
Joke: (MC - 0 - 11) A teacher drew several circles on a sheet of paper. Then he asked a student "How many circles are there?" "Seven" was the answer. "Correct! So how many circles are there?" the teacher asked another student. "Five," answered the student. "Absolutely right!" replied the teacher. How many circles where there on the sheet?
Answer: 12, 7 on one side and 5 on another - Ask your parents
(Manas contributed) Draw one line to make 5 + 5 + 5 = 550. You can't touch the "=" sign
Answer: 545+5=550
(Moscow - 10) Some soldiers need to cross a river. They spot 2 boys playing with a rowboat. However the boat is tiny and can only hold 2 boys or one soldier. How do they all cross the river?
Instructor Note: Use beads of two colors for soldiers and boys. Lead younger kids through "only possibility" argument.
(Moscow - 11) Wolf, Goat and Cabbage river crossing - A man has to take a wolf, goat and cabbage across the river. The boat has enough room for the man and one of the wolf/goat/cabbage. Wolf eats goat, Goat eats cabbage, unless the man is with them. How do they cross the river?
Take Goat, Come back, Take cabbage, Bring Goat, Take Wolf, Come back, Take Goat
Instructor Note: Lead younger kids through the "only possibility" argument
Homework - (Smiti contributed) - There are three baby penguins and each's father penguin on one side of river. There is a boat which can carry two penguins at a time. No baby penguin should be left without its own father when another father is around. How will all six cross the river.
References: More Puzzles, by Shakuntala Devi
Mathematical Circles (Russian Experience), by Dmitri Fomin, Sergey Genkin, Ilia Itenberg
The Moscow Puzzles, by Boris A. Kordemsky
The Colossal Book of Short Puzzles and Problems, by Martin Gardner