Another, more thin, the proof of the same fact uses existence of the routes, allowing to bypass a course of a horse all cages of a chessboard, not having visited on one of them twice. As we already know, at such unitary detour by a horse of all cages of a chessboard ' black and white fields alternate. Clearly, what to place in tops of the broken line serving by a route of "round-the-world" travel, more than 32 horses are impossible. It is not less obvious, that at the most dense arrangement of horses in tops of a broken line the interval between them should make one top, that is all horses not attacking each other will settle down or only on black, or only on white fields

Set becomes employment not only fascinating but also demanding time.

To find the sum of the numbers standing on any diagonal from the beginning to a place interesting us, it is enough to look at the number located from below and to the left of last composed. Let, for example, we wish to calculate the sum of numbers of a natural number from 1 to 9. "Having gone down" on a diagonal to number 9, we will see, that below it at the left there is number 45. It also gives the required sum

On fig. 128 11 various figures geksamino which can serve as cube development are represented. It is curious, that how many we tried, to combine from these figures a rectangle the area in 66 individual squares to all of us equally it will not be possible (though, perhaps, these 11 geksamino keep within more interesting figures). Thus, among 35 various geksamino 11 of "cube developmentВ» form the most discouraging set

Cubic sides. They also limit a hypercube, forming its hypersurface.

Though the impossibility proof trisektsii a corner by means of compasses and a ruler does not leave any doubts at those who understands it, all over the world still there are fans who amuse itself hope as if all of them managed to solve a problem and to observe thus all requirements. Typical "trisek-trist", as a rule, understands elementary geometry enough to invent the way of "decision" of an unsoluble problem, but insufficiently well owns mathematics to track up to the end the impossibility proof trisektsii or to find out an error in the reasonings

* Mathematical Puzzles of Sam Loyd, selected and edited by M. Gardner, N. Y., vol

The most part of errors Djudeni has been noticed by readers of its magazine and departments of puzzles and entertainments whom it conducted in various newspapers. It has allowed Djudeni to make corrections before to publish collections of the problems. However and in its books there are many erroneous decisions. We will consider, for example, the following problem — a version of known problems about detour by a chessboard castle

The girl has sat down in a boat and has departured to the lake centre where an anchor there was a raft. Unlucky Romeo has solved dozhts. To be given ashore. В«Sooner or later to it all the same prts

"Sprjamljaemost" 35 figures geksamino (each of which consists of 6 squares) till now in detail it is not investigated, though group, rukovodimaja Spirom, has come to conclusion, that the number straightened geksamino is equal

Best of known decisions belongs a banner nitomu to the English composer of puzzles Genr! E.Djudeni also demands 36 courses. Let figure meaning number of a small square which moves at ochered nom a course. Then sequence of courses in resheni! Djudeni looks so: 12543 12376 12376 12375 48121 65765 84785 6

The identical squares, adjoining the friend I to the friend as chessboard cages, it is possible pokryja a plane. In the same way all space can zja be made look fat identical cubes. As odina kovd equipotential triangles allow zamostit plov a bone is not worse at all, than squares, can pokazatja that n with identical correct tetrahedrons mozhl fill entirely all space. It seems vja so much obvious, that long time of "ability" tyoja raedra did not cause any doubts

Chinchilla (Chinchilla laniger) — the average size a rodent with dense fluffy bluish-grey fur. Occupies high mountains of the Andes in Chile and Bolivias. Lives colonies among rocks. Eats various plants

Magot (Masasa sylvana) — a unique kind of a sort of the macaques living in Africa (other kinds including Tselebessky macaque Masasa mentioned in the text maurus, live in Asia). In an antiquity, apparently, has been delivered to Southern Europe, but up to now has remained only on rocks of Gibraltar where it is now artificial it is supported by constant delivery from Africa.

Here difficulty of doctoring of wild animals also consists in it. Many of them, it is possible to tell, conceal the illness, illness first signs are shown only when already anything or nearly so will make nothing. I remember a case with one pichugoj. Right after sunrise she has well eaten, then all the morning long cheerfully chirped, and at three o'clock in the afternoon was already dead, and until the last minute nobody has noticed anything wrong

The unique inhabitant of pavilion of reptiles who did not leave the weight category, how many it ate, — gviansky a dragon, by name of George, the representative of very interesting sort of the lizards living in the north of the South America. At gvianskih dragons a large powerful head with the big clever eyes, at length they reach two foots of six inches, their trunk and a tail remind

But here absolutely smerklos, zarjanka finishes to sing and flies to spend the night on a mimosa. All day sounds have ceased, for short time the silence previous night voices sets in. The first invariably begin owls. Here someone zashchelkal a beak, is heard a crash as if tear a calico, are white-faced spljushki; long, with perelivami, udpvlen -

— Va! — he has sadly exclaimed, sipping whisky. — it is very a pity to me, that you leave from Bafuta, my friend.

It was impossible to name the first smoking stunning good luck. All our extraction have made a little podkovono-syh bats with muzzles as at the modelled monsters, three huge multilegs — the such Frankfurt sausages edged from below by legs — yes the small grey sleepyhead who has snatched the hunter for a finger and has got away. We have collected networks, have put out a fire and have gone further. The following hollow tree was much more above and more thickly the first