536 Puzzles and Curious Problems

368 Answers reaching one of the corner I's we have the option of ending in the extreme corner or going backwards to an E diagona ...

Answers 369 RAILWAY ROUTES There are 2,501 ways of going from B to D, as follows: I-line journey I route 2 variations 2 2-line ...

370 Answers SIXTEEN STRAIGHT RUNS The illustration shows how the traveller could have driven his car 76 miles in sixteen strai ...

Answers 371 then get to the right of C. Also the route from D to D then becomes evident, as does that from B to B, and the rest ...

372 Answers strokes, starting from A and ending at Z. Places in the figure are purposely not joined up, in order to make the rou ...

Answers 373 A HOPSCOTCH PUZZLE The hopscotch puzzle may be drawn in one continuous line without taking the pencil off the pape ...

374 Answers A TREE PLANTING PUZZLE The illustration shows the graceful manner of planting the trees so as to get nine rows wit ...

Answers 375 A PEG PUZZLE ~........ ',". · .. 3/.. · ·. . '~;"'....... ". ~ • \, \ • ''&f. I"" • • : ''Q.o/ ". • .. ~, • : ...

376 Answers DEPLOYING BATTLESHIPS •••• The illustration shows that the ships form five lines with four in every line, and the ...

Answers 377 THE FOUR-COLOR MAP THEOREM With two or more contiguous countries, two colors at least are obviously necessary (Fig ...

378 Answers country were contiguous with each of four that are contiguous each with each. If such a map is possible, the theorem ...

Answers 379 It is now clear that, at each successive addition of a new country, all the countries previously drawn must be conti ...

380 Answers A SW ASTIKLAND MAP ~ A - C r-- B I Three different colors are necessary. The bottom right-hand corner of the ...

Answers 381 in 3 ways, two in 3 ways, and three in I way, making together 7 ways, which is the same as the cube of 2 less l. A ...

382 Answers Add these seven results together and you get 1,733,760, which deducted from the number first given above leaves 1,89 ...

Answers 383 A GOLF COMPETITION PUZZLE The players may be paired and arranged as follows: ROUNDS 1 2- 3 4 5 l"LINHS Be BF SF CE ...

384 Answers 16,23,25, and 31 inches from one end. Another solution is I, I, I, 1,6,6,6,6,5. This puzzle may be solved in, at few ...

Answers 385 plained, and the others give only four solutions each. There are, therefore, in all, forty-eight different ways in w ...

386 Answers FLIES ON WINDOW PANES The three lively flies have taken up new positions, as indicated by the arrows, and still no ...

Answers 387 the chapter on "The Calculus of Finite Differences" in my book New Mathe- matical Diversionsfrom Scientific American ...