by Dudeney, Henry Ernest, 1857-1930
Available in 215 free installments
Owner:
The diagrams will show how the figures are constructed?each with the seven Tangrams. It will be noticed that in both cases the head, hat, and arm are precisely alike, and the width at the base of the body the same. But this body contains four pieces in the first case, and in the second design only three. The first is larger than the second by exactly that narrow strip indicated by the dotted line between A and B. This strip is therefore exactly equal in area to the piece forming the foot in the other design, though when thus distributed along the side of the body the increased dimension is not easily apparent to the eye.
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170.?THE CUSHION COVERS.? solution
The two pieces of brocade marked A will fit together and form one perfect square cushion top, and the two pieces marked B will form the other.
171.?THE BANNER PUZZLE.? solution
The illustration explains itself. Divide the bunting into 25 squares (because this number is the sum of two other squares?16 and 9), and then cut along the thick lines. The two pieces marked A form one square, and the two pieces marked B form the other.
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172.?MRS. SMILEVS CHRISTMAS PRESENT.? solution
The first step is to find six different square numbers that sum to 196. For example, 1+4 + 25 + 36+49 + 81 = 196; 1 +4 + 9 + 25 + 36 + 121 = 196; 1 +9 + 16 + 25 + 64 + 81 =196. The rest calls for individual judgment and ingenuity, and no definite rules can be given for procedure. The annexed diagrams will show solutions for the first two cases stated. Of course the three pieces marked A and those marked B will fit together and form a square in each case. The assembling of the parts may be slightly varied, and the reader may be interested in finding a solution for the third set of squares I have given.
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173.?MRS. PERKINS'S QUILT.? solution
The following diagram shows how the quilt should be constructed.
There is, I believe, practically only one solution to this puzzle. The fewest separate squares must be eleven. The portions must be of the sizes given, the three largest pieces must be arranged as shown, and the remaining group of eight squares maybe "reflected," but cannot be differently arranged.
174.?THE SQUARES OF BROCADE.? solution
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So far as I have been able to discover, there is only one possible solution to fulfil the conditions. The pieces fit together as in Diagram 1, Diagrams 2 and 3 showing how the two original squares are to be cut. It will be seen that the pieces A and C have each twenty chequers, and are therefore of equal area. Diagram 4 (built up with the dissected square No. 5) solves the puzzle, except for the small condition contained in the words, "I cut the twD squares in the manner desired." In this case the smaller square is preserved intact. Still I give it as an illustration of a feature of the puzzle. It is impossible in a problem of this kind to give a quarter-turn to any of the pieces if the pattern is to properly match, but (as in the case of F, in Diagram 4) we may give a symmetrical piece a half-turn ?that is, turn it upside down. Whether or not a piece may be given a quarter-turn, a half-turn, or no turn at all in these chequered problems, depends on the character of the design, on the material employed, and also on the form of the piece itself.
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175.^ANOTHER PATCHW ORK pi 1771 E.?solution
The lady need only unpick the stitches along the dark lines in the larger portion of patchwork, when the four p 9 1 81 pieces will fit together and form a square, as shown in our illustration.
