1676641341 counting sheep

counting sheep

counting sheep

To perform last week’s trick, the math magician need only choose his own secret number and mentally do what he told his audience to do. Our regular commentator Manuel Amorós confirmed it:

“I’ve done the Kruskal card counting trick several times and it often impresses the staff. It is based on the fact that whatever the number initially chosen is, if one follows the process described, it will eventually end in a certain letter (or a word if we are using text). Therefore, to perform the trick, the magician need only select a number in his mind and follow a process parallel to that of the volunteer, with almost complete certainty that after a certain period of time he will converge on it. This means that he must prolong the game for as long as possible and wait for the end of the card game to reveal the volunteer’s secret number.

And regarding the Kruskal brothers, Francisco Montesinos provides the following information:

“William wasn’t one-armed either. Along with Wallis, he was the creator of what is known as the Kruskal-Wallis test, which is widely used in nonparametric statistics — used when the parameters of the population from which a sample was extracted are unknown — to determine whether In View from them it can be argued that the available data belong to a single population or not.

Count sheep to avoid falling asleep

When we switch from counting cards to counting sheep (not to fall asleep, but quite the opposite: to keep our neurons wide awake), we find ourselves with a rich vein of mathematical puzzles from oral culture. Which is not surprising considering that arithmetic certainly evolved from cattle breeding just as geometry was fostered by agriculture. Hunter-gatherers wouldn’t care if a handful of berries contained 13 or 14 units, but a sheep more or less at the time of entry into the corral was information of paramount importance. So let’s look at three problems related to counting sheep, one very easy, one not so easy and one difficult.

The very simple is a classic I usually use to explain first degree systems of equations to children:

“Give me one of your sheep and I will have twice as many as you have,” says one shepherd to another.

“Give me one and we both have the same number,” replies the second.

How many sheep does each have?

In the not-so-simple one comes that marvelous calculator, which could determine with a simple glance how many sheep were in a flock, and which explained its ability by counting the legs and dividing them by 4. Our leg counter sees a flock and says to the shepherd:

—You have a lame sheep, I counted 59 legs.

“I have several cripples, although most of them are fine,” replies the pastor.

How many whole sheep and how many lame are there in the flock?

And I took the tough question from a book by the prolific French writer, essayist, and engineer Jean-Pierre Alem:

Two brothers sell a flock of sheep and collect a certain number of 10 euro notes, plus a tip, in 1 euro coins, less than 10 euros. Each sheep is worth as much as there are sheep. The brothers split the money up as follows: the eldest takes a 10-bill, the youngest takes another, and so on, until the eldest takes the last and the youngest takes the top. And since the younger brother earned a little less that way, the older brother takes one euro coins out of his pocket and gives them to him so that both are equal. How many coins did the older brother take out of his pocket?

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