Math practice. A summer BBQ.
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Eddie will be taking an entrance examination for seventh grade at the Kyiv Lycée. Here are sample problems from towards the end of three such tests.
Easy one:
Is 16^16 – 14^14 divisible by 10?
Harder one: It took me a full sheet of A3 sized paper to write the answer. I kept being interrupted, but still doubt I could have managed it in a timed test.
A lion and a tiger can eat a sheep in 2 hours
A lion and a wolf can eat a sheep in 3 hours
A tiger and a wolf can eat a sheep in 4 hours
How long does it take all three to eat a sheep?
Hardest one: Compute
Eddie had trouble with assumptions. The composers of the test obvious assume that the last figure involving repeating triads of digits must be the decimal representation of fractions. Even given that, you need to make a second assumption that the answer to the problem is an integer. Therefore the fraction should cancel one of the factors of either the big middle term or158. Another trick is recognizing that the huge middle expression can easily be simplified. I had a hard time convincing him.
Wanna throw these at American sixth graders? Good luck!
We had a typical summer BBQ on Saturday. Turnout was low – only got 12 RSVPs out of 30 invitations. Nonetheless the 17 of us had a great time. As a bonus we don't have to cook for a week. Afterwards we walked about three quarters of a mile to the beach. I felt I was doing pretty well carrying 28 lb Marianna most of the way. On the way back 50lb Zoriana also wanted a ride, and one of the guests carried her.
At his fifty years I could have done it. In a comment to my recent post about Naomi I wrote that at a similar age she had demanded, and ex-wife insisted as well, that I carry her a couple of miles. But I would not want to do it now!
That’s the news from a bucolic Lake WeBeGone, where I continue to plod away on two projects. Movie “The Greatest Self-Replicator” and a review of “Male-Female - the Origin of Human Sexual Differences.” The book is so rich that it keeps updating my notion for the video. Thank goodness nobody cares except me. I will get a speech out of it for next Saturday.
From my experience, arithmetic problems become meaningless if you learn equations in junior high school,
I think it was to train my intuition, or if I think about it, I think it was to make me like equations in junior high school.
According to a Japanese scholar who is familiar with animal viruses, he writes that E. coli also has something similar to a sex difference. I think it is better to limit the topic to human beings.
I just backed into a solution. Still can't prove it analytically.
Two bicyclists start out towards each other from cities A and B. They meet along the way. After they meet, it takes the first cyclist 9 hours to get to city B, and the second 4 hours to get to city A. How long did the two of them spend on the road, altogether?
After trying vainly to structure the problem, I selected a couple of different speeds for the cyclists to see what happened. A solution jumped out. I'm not going to recommend that Eddie try this tomorrow.
BTW: 21 2/3 hrs