The Magic of Logic (12)
A few more logical tasks for kids in Covid times
Social life in general has ground to a halt, for the grandkids group play is heavily restricted. We usually meet them in the garden. Strolling around in unusually beautiful November weather I give them some new logical problems. Here’s the first one this week:
A man needs to take two pills a day, one green and one white. Normally his wife puts them into a cup each morning for him to take. But she is going to be away for the weekend, so she puts four into the cup and leaves. Unfortunately she forgets that her husband is blind. The pills are exactly the same size and shape, and can only be distinguished by their colour. The husband is alone at home, and on each day he needs to take exactly one of each kind. How does he manage?
For an hour grandson Enders declared the problem impossible. Then suddenly he hit upon a possible strategy. After I confirmed he was on the right track it took him just minutes to work it out perfectly. His younger brother Hennes did not find it. Neither did a number of grown-ups I have tried the problem on. It is apparently unusually difficult. The solution is at the end of this article.
If you find the above problem too easy for your older kids, give them this version: The wife will be gone for four days and leaves four pairs for her husband in the cup.
How does he, blind as he is, ensure that he can take exactly one green and one white tablet, on each of the four days?
After having solved the first two-day problem Enders had no difficulty with this version. He told me the man should take three cups, and… Again, the solution is at the end of this article. But do try to solve it before you peek.
You must forgive me for constantly using Enders and Hennes for my stories: these days I cannot travel all over the world, plying super-smart kids with logical problems—as I have previously done. The grandkids are available, with suitable social distancing. Their parents are afraid of infections — them infecting us! If they catch COVID-19 in the school (which is currently open) they will in all likelihood get over it without serious problems. For the grandparents it could be deadly.
During the visit this week, in the garden, I asked Enders why the ground was covered in acorns. His answer came immediately: it happens every six years and is “because of evolution.” He also explained exactly why it was cyclical. I was testing to see if he understood the mechanisms in play, if he remembered the explanation I gave the kids a week earlier. He did, perfectly.
I tried another one: a man has a mechanical wall clock, which he has to wind up every day. One morning he discovered that he has forgotten to do so, and the clock has stopped. So he winds it, but does not have any other clock or watch in his house, no radio or telephone, to set the time correctly.
There is a public clock on the town square. How can he get the time, how can he synchronize his clock with the one which is maybe a mile away, which he cannot see?
Enders told me how immediately, but confessed he remembered the problem from two years earlier. This kid forgets nothing!
You should try to solve this problem, dear reader. And the promised solutions to the pill problems above? I cannot bring myself to reveal it yet. I will add both solutions here at some time in the future!
October 2024: the future is here, and the answers to the pill problems is fairly straightforward. With the four pills, the man breaks each in half, putting one half into one cup and the other into a second cup. That insures that there will be a full green and a full white pill in each cup.
With eight pills for four days the strategy is the same: he breaks each into four quarters and put the quarters into four cups. That results into a full tablet of each colour being present in each cup.
And setting the wall clock to the time on the village clock? The man winds up his clock and sets it to 12:00 noon. He then walks to the village and checks the chock there. Say it is showing 1:30 pm. Then he walks back to his house and sets his clock to 3 pm. Get it?
