Cigarettes in touch | THE GAME OF SCIENCE | EUROtoday

To our claustrophobic traveler final week, it must be climbed into the final automobile. At first look plainly it does not matter a automobile as one other; But because the tunnel is on the exit of the station, the practice will nonetheless be accelerating when getting into it, so the final automobile will cross it sooner than the others. In addition, as Salva Fuster and Francisco Montesinos, the traveler, have identified, on the time of getting into the tunnel, it may run ahead, in order that their very own velocity will add to that of the practice to present a better relative crossing velocity.

In the case of the steadiness of unequal arms, it’s a lure query (we should not overlook that they’re issues posed by a malevolent little one): the reply is sure … at any time when it’s from the geometric imply and never of the arithmetic, as we are likely to suppose when it’s stated “the average” to dry.

As for the issue of sq. chips, it gave rise to quite a few feedback and alternative ways of addressing it. The easiest, elegant and ingenious is the proposed by Manuel Amorós. Calling a y b to the variety of bins on the aspect of 1 and the opposite sq., and n To the variety of chips, we’ve got to:

n + 7 = a²

n – 10 = b²

With which, subtracting the second equality of the primary:

(a + b)(a – b) = 17

the place it follows that A + B = 17, A – B = 1

so n = 74

For those that are too concise of improvement, do not forget that of “sum for difference, difference of squares”, and that 17, being cousin, can solely be damaged into two elements of the shape 17 = 1 x 17.

And an equally temporary and stylish answer is the one supplied by María Luisa González to the variant with dominoes:

A sq. with dominoes is fashioned with x x 2x chips, subsequently:

(X x 2X) – 1 = (X – 1)(2X – 2) + 13

The answer is that the primary sq. I did it with 4×8 chips (and I lacked 1) and the second with 3×6 and I’ve 13. I’ve 31 chips.

Cooked riddles

In the jargon of the followers of logical-mathematical riddles, when somebody discovers a greater or completely different answer from the “official”, it’s stated that they’ve “cooked” the issue. For instance, Fuster and Montesinos have given one other boil to that of the Cloustrophobic traveler by mentioning that, along with climbing within the final automobile, he can run ahead to attenuate the time of permanence within the tunnel. And Luis Miguel Barros feedback that his fifteen -year -old daughter noticed that, since it’s not specified within the assertion, the sq. of dominoes doesn’t must be crammed: it may be a body body, which seems new and fascinating options. And Ignacio Alonso factors out that possibly the Cloustrophobic traveler prefers to cross the unhealthy drink as quickly as doable, which might go for the primary automobile.

One of essentially the most well-known cooked issues (which we’ve got already talked about a couple of years in the past) is that of cigarettes in touch. For a time it was thought that 6 was the utmost variety of cigarettes that might be organized so that every one touched everybody else, as indicated within the determine; But then an answer with 7 appeared (can you discover it?).

And from the easy cooking, mathematical delicacies was handed, as a result of somebody puzzled what number of equal cylinders might contact if their ends couldn’t be used, that’s, in the event that they had been of infinite size (what number of do you suppose they’re?).

And, as soon as once more, what appeared like a easy mathematical leisure proved to be associated to auxetic supplies, that are those with a coefficient of Poisson Negative, that’s, opposite to what occurs with an elastic rubber or a gum, they widen when stretching them as an alternative of narrowing. But that’s one other article …