http://www.m516.com/pearls-necklace/
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 7 8mm White Akoya Cultured Pearl Necklace 25 $1.79 (3 Bids) Time Remaining: 30m |
 big 25mm white Freshwater Pearls necklace dragon j7626 $45.00 Time Remaining: 30m Buy It Now for only: $45.00 |
 Stunning Blue Stone Pearl 14Kt Gold Bead 24 Necklace $99.95 Time Remaining: 30m Buy It Now for only: $99.95 |
 17 20 8 9mm 3 Row Freshwater Pearl Necklace WGP Strand $12.25 (15 Bids) Time Remaining: 31m |
 pearls bowknot Wedding necklace Bracelet Set White GP Swarovski clear Crystal $9.99 Time Remaining: 31m |
 HUGE 48 11 12mm Genuine White Baroque Pearl Necklace CHRISTMAS GIFT $0.99 Time Remaining: 31m |
 Wedding Bridal pearl Crystal Necklace Earring Set S125 $9.99 Time Remaining: 31m |
 46 7 10mm Multi Color Freshwater akoya Pearl Necklace A 26 $5.95 Time Remaining: 31m |
 rare 11 12mmAAA South Sea GOLDEN PEARL NECKLACE 18 $288.00 Time Remaining: 31m Buy It Now for only: $288.00 |
 Vintage Silvertone Mod Floral Cross Choker Necklace Adjustable Chain Faux Pearl $24.60 Time Remaining: 32m Buy It Now for only: $24.60 |
 Pink Pearl Jewellery Necklace Earring Set $3.25 (3 Bids) Time Remaining: 32m |
 80 acrylic plastic faux imitation pearl for necklace round bead 8mm Burgundy $3.50 Time Remaining: 32m |
 14K BAROQUE PEARLS NECKLACE AND BRACELET SET $35.00 Time Remaining: 32m |
 Elegant White Shell Pearl necklace 10MM E162 $0.10 (1 Bid) Time Remaining: 32m |
 Pop Hellokitty KT Pearl Necklace Bracelet Bangle Ring Set Kid Girl Gift PA03 $0.89 Time Remaining: 32m |
 8mm Silver Gray Sea Shell Pearl NECKLACE 175 $2.25 (4 Bids) Time Remaining: 32m |
 New Excellent Wine Red Pearl Pendant Necklace $1.55 (2 Bids) Time Remaining: 33m |
 AA+ 10 11 MM AKOYA White Pearl Necklace 18gift box $69.00 Time Remaining: 33m Buy It Now for only: $69.00 |
 WHITE IVORY Pearl Necklace Set Costume Jewelry Bridal $17.99 Time Remaining: 33m Buy It Now for only: $19.99 |
 CHUNKY PURPLE ICE Bead Necklace Pearl Earring SET COSTUME JEWELRY $14.99 Time Remaining: 33m Buy It Now for only: $16.99 |
 Silver Blue PEARL Black Bead NECKLACE EARRING SET $15.99 Time Remaining: 33m Buy It Now for only: $17.99 |
 PURPLE PINK CHUNKY Pearl Necklace Earring SET 21 $9.99 Time Remaining: 33m Buy It Now for only: $12.99 |
 Bib MOTHER OF PEARL GLITTER SHELL NECKLACE EARRING SET $12.99 Time Remaining: 33m Buy It Now for only: $17.99 |
 Chunky WHITE PEARL CRYSTAL NECKLACE EARRING SET $16.99 Time Remaining: 33m Buy It Now for only: $18.99 |
 2 STRAND Silver Pearl GLASS BEAD NECKLACE EARRING SET $12.99 Time Remaining: 33m Buy It Now for only: $14.99 |
 SILVER Pearl Glass Bead Necklace Earring Set Bridal $15.99 Time Remaining: 33m Buy It Now for only: $17.99 |
 BRONZE CREAM TAUPE CHUNKY PEARL NECKLACE EARRING SET $9.99 Time Remaining: 33m Buy It Now for only: $12.99 |
 WHITE PEARL HEART Flower Necklace EARRING SET Bridal $19.99 Time Remaining: 33m Buy It Now for only: $21.99 |
 SILVER Black Pearl Rhinestone Necklace Set Costume $19.99 Time Remaining: 33m Buy It Now for only: $21.99 |
 SILVER GRAY PEARL GLASS BEAD NECKLACE EARRING SET $16.99 Time Remaining: 33m Buy It Now for only: $18.99 |
 BRONZE PEARL GOLD CRYSTAL NECKLACE SET Costume Jewelry $16.99 Time Remaining: 33m Buy It Now for only: $18.99 |
 CHUNKY BLUE ICE NECKLACE TEAL PEARL EARRING SET COSTUME JEWELRY $14.99 Time Remaining: 33m Buy It Now for only: $16.99 |
 WHITE PEARL NECKLACE EARRING SET Crystal Glass Bridal $18.99 Time Remaining: 33m Buy It Now for only: $21.99 |
 10mm Chocolate South Sea Shell Pearl Necklace 18 $2.25 (2 Bids) Time Remaining: 33m |
 Lapis Lazuli stone and golden freshwater pearl necklace with matching earrings $14.99 Time Remaining: 34m Buy It Now for only: $16.50 |
 Silver Plated Bridal Pearl Crystal Earrings Necklace FASHION $4.89 Time Remaining: 34m Buy It Now for only: $5.38 |
 Italian Designer LUISA DELLA SALDA Designer Pink Rose Quartz and Pearl Necklace $69.99 Time Remaining: 34m |
 A12 24 FASHION PEARL NECKLACE AS IS $2.75 Time Remaining: 34m Buy It Now for only: $2.75 |
 18K GP Pearl Necklace Used Swarovski Crystal Pendant $0.01 Time Remaining: 34m |
 Genuine Natural 6mm white Pearl Necklace 100 $31.99 Time Remaining: 34m Buy It Now for only: $31.99 |
 2 rows Black White Pearl necklace Bracelet Earrings $0.99 Time Remaining: 34m |
 200 AAA grade 65mm white AKOYA pearls necklace $217.00 Time Remaining: 34m Buy It Now for only: $217.00 |
 Art Nouveau Sterling Silver Pearl Mother of Pearl Garnet Pendant Necklace $14.95 Time Remaining: 34m |
 White Pearl Jade Butterfly Pendant Necklace Earrings $0.01 Time Remaining: 34m |
 Selini Baroque Pearl Aurora Borealis 2 Strand Necklace $12.75 (1 Bid) Time Remaining: 34m |
 12k Gold Filled NECKLACE WITH FAUX PEARL ACCENT $3.99 Time Remaining: 35m |
 Fashion Golden Circle Inlay White Pearl Beads Black Rope Necklace $5.99 (1 Bid) Time Remaining: 35m |
 HUGE ABALONE SHELL+BIWA PEARL+RIVER PEARL+Amethyst Necklace 17 B2526 $23.05 (11 Bids) Time Remaining: 35m |
 35 65mm AAA GRADE YELLOW AKOYA PEARLS NECKLACE 14KT $146.00 Time Remaining: 35m Buy It Now for only: $146.00 |
 ELEGANT 17 White Crystal Black MOP FW Pearl Necklace GREAT GIFT $0.99 Time Remaining: 35m |
 Women Girl Accessories Flower Lace Pearl Imitation Long Necklace Pink $8.00 Time Remaining: 35m Buy It Now for only: $8.00 |
 2pc Pearl Shell Bead Pendant For Necklace 55x44mm F0032 $6.80 Time Remaining: 35m Buy It Now for only: $6.80 |
 NEW 14mm Round Chocolate Shell Pearl Pendant Necklace OVER 99 SATISFIED $0.99 Time Remaining: 35m |
 Gorgeous Large Festive Fancy Clustered Ivory Faux Pearl Ribbon Bib Necklace $2.99 Time Remaining: 36m |
 VTG Blue Cabochon Rhinestone and faux Pearl necklace $19.99 Time Remaining: 36m |
 Elegant 17 Brown Pearl Necklace w Lobster Clasp FINDINGJEWELRY $0.99 Time Remaining: 36m |
 12MM shell pearl necklace Crystal clasp $16.00 Time Remaining: 36m Buy It Now for only: $16.00 |
 Retired lia sophia Moon Dance Necklace Genuine Mother of Pearl RV 5800 $17.00 (6 Bids) Time Remaining: 36m |
 GORGEOUS 2882gms MULTI PEARL GARNET CITRIN ROSEQUARTZ Sterling Silver Necklace $49.99 Time Remaining: 36m |
 Genuine 10mm round white pearl necklace ladybug 925sc c $25.00 Time Remaining: 36m Buy It Now for only: $25.00 |
 4800 9 10MM white Akoya Cultured Pearl Necklace earring set 18 AA $5.02 (7 Bids) Time Remaining: 36m |
 Sterling Silver 8 85mm Pearl Stud Earrings Necklace $39.99 Time Remaining: 36m Buy It Now for only: $39.99 |
 Charming8 9mm White Akoya Culture Pearl Necklace 25 $0.95 Time Remaining: 36m |
 7 8MM White Akoya Pearl Necklace AAA 18 AA $3.31 (5 Bids) Time Remaining: 36m |
 Fancy Charming Starriness Yellow Pearl Necklace $11.68 Time Remaining: 37m Buy It Now for only: $11.68 |
 LARGE HAND KNOTTED RED WHITE GLASS PEARL NECKLACE EARRINGS OLD STOCK $11.95 (1 Bid) Time Remaining: 37m |
 Bridal Ribbon Ivory Color Faux Pearl Necklace Set S1195 $19.50 Time Remaining: 37m |
 Exciting 7 8MM White Akoya Pearl Necklace 2 rows 17 18 $12.99 Time Remaining: 37m Buy It Now for only: $12.99 |
 Genuine 17 2row 11mm round white pearls necklace $76.00 Time Remaining: 37m Buy It Now for only: $76.00 |
 8mm Pink South Sea Shell Pearl Necklace 18 $1.04 (3 Bids) Time Remaining: 37m |
 beautiful gray shell Pearl Pendant Necklace E524 $0.10 Time Remaining: 38m |
 HUGE AMETHYST+BIWA PEARL NECKLACE 21 1 2 B3034 $31.00 (10 Bids) Time Remaining: 38m |
 Charming Black pearl pendant necklace 175 $6.99 Time Remaining: 38m |
 3Strand Pearl AB AUSTRIAN Crystal queen Crown Necklace $13.91 Time Remaining: 38m Buy It Now for only: $13.91 |
 Beautiful 35 7 75mm Freshwater Black Pearl Necklace LOW PRICE HIGH QUALITY $0.99 Time Remaining: 38m |
 South Sea Golden Pearl Necklace 12x124mm 99x102mm 14k Yellow Gold Clasp $3,960.00 Time Remaining: 39m Buy It Now for only: $3,960.00 |
 VINTAGE LES BERNARD DESIGNER SIGN FAUX PEARL NECKLACE STUNNING $149.50 Time Remaining: 39m Buy It Now for only: $149.50 |
 Tahitian Black Round Pearl Necklace 118mm 100mm $4,400.00 Time Remaining: 39m Buy It Now for only: $4,400.00 |
 Vintage Necklace Chunky Peach MOTHER OF PEARL Shell Orange Red White Pretty $5.00 Time Remaining: 39m |
 18 10 11mm Multi Color Freshwater Pearl Necklace WCCB Off Round Dyed Color $18.00 Time Remaining: 40m Buy It Now for only: $18.00 |
 Gorgeous 80 Multi Color Freshwater Pearl Rope Necklace Strand $32.00 Time Remaining: 40m Buy It Now for only: $32.00 |
 DEAD PAWN TURQUOISE AND SILVER HEISHI BEAD MOTHER OF PEARL EAGLE FETISH NECKLACE $99.00 Time Remaining: 40m Buy It Now for only: $99.00 |
 64 SILVER FRESHWATER PEARL NECKLACE $32.95 Time Remaining: 40m Buy It Now for only: $32.95 |
 GOLDEN KESHI PEARL NECKLACE w 18KYG CLASP w DIAMONDS $3,500.00 Time Remaining: 40m Buy It Now for only: $3,500.00 |
 VINTAGE ESTATE AQUA GREEN JAPAN DEMI SET2 STRAND Pearl Necklace Earrings $22.32 Time Remaining: 40m Buy It Now for only: $22.32 |
 X35 Long 7 8mm Natural White Freshwater Pearl necklace 32 $0.01 Time Remaining: 40m |
 LONG HANDMADE MOTHER OF Pearl White SILVER BEIGE SEED BEAD necklace $14.95 Time Remaining: 40m Buy It Now for only: $14.95 |
 18 22 3 Strds Genuine White Freshwater Pearl Necklace FINDINGJEWELRY $0.99 Time Remaining: 40m |
 22 24 2Row 6 7mm Gray Freshwater Pearl Necklace X2092 $26.00 Time Remaining: 40m Buy It Now for only: $26.00 |
 VINTAGE LOT OF COSTUME FAUX PEARL 2 NECKLACES 2 FAUX Pearl Earrings $2.42 (3 Bids) Time Remaining: 40m |
 52 4 10mm Purple Graduated Freshwater Pearl Necklace $20.00 Time Remaining: 41m Buy It Now for only: $20.00 |
How to divide a black and white pearl necklace Puzzle!?!?
Find the solution for the following: Two robbers steal a valuable necklace of black and white pearls. There are even numbers of white and black pearls in the necklace. The pearls are evenly spaced, however, the colors are not necessarily alternating or even symmetric.
Provide a convincing argument that no matter what the necklace looks like, it is always possible to cut it into two pieces each having half the black and half the white pearls.
consider a vertical diametrical cut AB [imaginary]
from top to bottom in between beads
let us focus on one colour, say white pearls and on one half,
say clockwise between A & B [ THE half ]
suppose THE half contains less than half the white pearls
it is obvious that if the imaginary cut is rotated through 180°,
THE half will now contain more than half the white pearls
rotate the cut clockwise bead by bead [ a MOVE]
a MOVE may result in
(a) no change [ 0 decrease in deficit]
(b) an increase in deficit [ -1 decrease in deficit]
(c) a decrease in deficit [ 1 decrease in deficit]
one MOVE can reduce the deficit by a MAXIMUM of one,
so it follows that in moving from a deficit state to a surplus state,
there has to be a cut where there is neither deficit nor surplus
make the imaginary cut real at this point !
Pearl Necklace - ZZ Top