irish mathematical olympiads 1988 - 2013

... Suppose that n is p-partitionable. Prove that p divides n or n + 1. (b) Suppose that n is divisible by 2p. Prove that n is p-partitionable. 21 diendantoanhoc.net [VMF] 18th Irish Mathematical Olympiad 7 ... diagonal intersect? 13 diendantoanhoc.net [VMF] 1st Irish Mathematical Olympiad 30 April 1988, Paper 2 1. The triangles ABG and AEF are in the same plane. Between them the followi...

Ngày tải lên: 29/06/2014, 11:07

... KL d/ S ABKI = ½ AB.(AI + BK) - Bài IV: y= (m-1)x + 6m - 1991 = mx – x + 6m - 1991 = m (x + 6) – 1991 => Nếu x = - 6 thì y = - 1991 + 6 = - 1985 Vậy ta có A (-6 ; - 1985) cố định. …………………………………………………………………………………………………… ... bng nhau). - Bi IV: M = ( 2x - 1) 2 3 |2x-1| + 2 = (| 2x 1|) 2 3 |2x-1| + 9 4 - 1 4 = ( |2x 1| 3 2 ) 2 - 1 4...

Ngày tải lên: 25/01/2014, 14:23

... nhau). - Bài IV: M = ( 2x - 1) 2 – 3 |2x-1| + 2 = (| 2x – 1|) 2 – 3 |2x-1| + 9 4 - 1 4 = ( |2x – 1| – 3 2 ) 2 - 1 4 ≥ - 1 4 Dấu “ = ” xảy ra khi ( |2x – 1| – 3 2 ) 2 = 0  | 2x - ... GTLN. GI í GII 200 0- 2001 Bi I: 1/ P = 1 x 2/ x= 6-2 5 = ( 5 -1 ) 2 => P = 2 - 5 3/ P.( nxx +>+ )1 ( 1 x )( 1x + ) > x n+ 1- x > x n+...

Ngày tải lên: 29/05/2014, 15:23

... quadrilateral whose cir- cumradius equals those of the triangles AN K and CLM. Find the 36 Preface This book is a continuation of Mathematical Olympiads 199 6-1 997: Olym- piad Problems from Around ... A i is not connected via a diag- onal to any other point of this polygon, so we have 0 diagonals from A i , an even number. Finally evenly many diagonals inside this poly- gon stem from A...

Ngày tải lên: 02/06/2014, 16:30

... Combining this with our upper bound for x, we see that the only possible values for x are -1 6 and -1 7. However, only -1 7 yields an integral value of y, and we get the unique solution (x, y) = (−17, 12). Problem ... hour hand. Prove that at some moment, the former sum is greater than the latter sum. Problem 8 A set S of three-digit numbers formed from the digits 1, 2, 3, 4, 5, 6 (p...

Ngày tải lên: 02/06/2014, 16:33

... cos[(k 2 − 1)θ]. By the product-to-sum formulas, we derive cos[(2k + 1)θ] − cos θ 2 = cos[(2k 2 − 1)θ] − cos θ 2 or cos[(2k + 1)θ] − cos[(2k 2 − 1)θ] = 0. By the sum-to-product formulas, we obtain 2 ... edge connecting them are darkened.) To show that any 6-terminal network has a 1-mill, we note that any complete set of three terminals is a 1-mill. We again work by contradiction. Any terminal...

Ngày tải lên: 05/06/2014, 19:02

... bng nhau). - Bi IV: M = ( 2x - 1) 2 3 |2x-1| + 2 = (| 2x 1|) 2 3 |2x-1| + 9 4 - 1 4 = ( |2x 1| 3 2 ) 2 - 1 4 - 1 4 Du = xy ra khi ( |2x 1| 3 2 ) 2 = 0 | 2x - 1| = 3 2 ... GTLN. GI í GII 200 0- 2001 Bi I: 1/ P = 1 x 2/ x= 6-2 5 = ( 5 -1 ) 2 => P = 2 - 5 3/ P.( nxx +>+ )1 ( 1 x )( 1x + ) > x n+ 1- x > x n+ x + x...

Ngày tải lên: 17/12/2013, 18:13

... call (800) 81 0-4 145, ext. 5000, or e-mail special.markets@perseusbooks.com. Library of Congress Control Number: 2012924095 97 8-0 -4 6 5-0 659 9-8 (e-book ISBN) Printed in Great Britain in 2013 by Profile ... exist? Until the Bailey-Borwein-Plouffe formula was found, no one imagined it could be done in binary. VISIONS OF INFINITY the distant, low-lying oceans. But this ever-chang...

Ngày tải lên: 03/05/2014, 19:30

... under the Irish Bank Resolution Corporation Act 2013. ”. 2 ______________________ AN BILLE FÁ CHORPARÁID NA HÉIREANNACH UM RÉITEACH BAINC, 2013 IRISH BANK RESOLUTION CORPORATION BILL 2013 ______________________ ... the Irish Bank Resolution Corporation Act 2013, ”, and (c) in Regulation 9(2), by substituting “a special liquidator appointed under section 7 of the Irish...

Ngày tải lên: 01/07/2014, 16:05

... hoạt động tín dụng cá nhân của ngân hàng đầu tư và phát triển Việt Nam ( BIDV )- chi nhánh Bình Định giai đoạn 2011 - 2013 . SVTH: NGUYỄN HỒ ANH TÚ Trang 1 GVHD: Ts. BÙI ANH SƠN NĂM 2011 Nợ quá ... Định giai đoạn 200 8-2 010. SVTH: NGUYỄN HỒ ANH TÚ Trang 34 GVHD: Ts. BÙI ANH SƠN NĂM 2011 Bảng 2.3: cơ cấu hoạt động tín dụng của Ngân Hàng BIDV-chi nhánh Bình Định giai đoạn 200 8-2...

Ngày tải lên: 17/09/2012, 16:44