1![The 58th William Lowell Putnam Mathematical Competition Saturday, December 6, 1997 A–1 A rectangle, HOMF, has sides HO = 11 and OM = 5. A triangle ABC has H as the intersection of the altitudes, O the center of the cir The 58th William Lowell Putnam Mathematical Competition Saturday, December 6, 1997 A–1 A rectangle, HOMF, has sides HO = 11 and OM = 5. A triangle ABC has H as the intersection of the altitudes, O the center of the cir](https://www.pdfsearch.io/img/51e119546e02f417207cee54527f3fe4.jpg) | Add to Reading ListSource URL: kskedlaya.org- Date: 2014-01-16 17:22:37
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2![The 57th William Lowell Putnam Mathematical Competition Saturday, December 7, 1996 A–1 Find the least number A such that for any two squares of combined area 1, a rectangle of area A exists such that the two squares ca The 57th William Lowell Putnam Mathematical Competition Saturday, December 7, 1996 A–1 Find the least number A such that for any two squares of combined area 1, a rectangle of area A exists such that the two squares ca](https://www.pdfsearch.io/img/ccfc23e9020160113f99a770b2668118.jpg) | Add to Reading ListSource URL: kskedlaya.org- Date: 2014-01-16 17:22:33
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3![Lastname Agundez Amundsen Apai Auclair-Desrotour Bailey Lastname Agundez Amundsen Apai Auclair-Desrotour Bailey](https://www.pdfsearch.io/img/b45b79e509abae55e0c493c8334d635e.jpg) | Add to Reading ListSource URL: www.exoclimes.orgLanguage: English - Date: 2016-07-23 03:02:12
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4![The 69th William Lowell Putnam Mathematical Competition Saturday, December 6, 2008 A–1 Let f : R2 → R be a function such that f (x, y)+ f (y, z)+ f (z, x) = 0 for all real numbers x, y, and z. Prove that there exists The 69th William Lowell Putnam Mathematical Competition Saturday, December 6, 2008 A–1 Let f : R2 → R be a function such that f (x, y)+ f (y, z)+ f (z, x) = 0 for all real numbers x, y, and z. Prove that there exists](https://www.pdfsearch.io/img/8a148ff26a305d5ca4c9cadd93da336a.jpg) | Add to Reading ListSource URL: kskedlaya.orgLanguage: English - Date: 2014-01-16 17:23:35
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5![The 74th William Lowell Putnam Mathematical Competition Saturday, December 7, 2013 A1 Recall that a regular icosahedron is a convex polyhedron having 12 vertices and 20 faces; the faces are congruent equilateral triangle The 74th William Lowell Putnam Mathematical Competition Saturday, December 7, 2013 A1 Recall that a regular icosahedron is a convex polyhedron having 12 vertices and 20 faces; the faces are congruent equilateral triangle](https://www.pdfsearch.io/img/118fa5fd15354dd5850bdc8744f69345.jpg) | Add to Reading ListSource URL: kskedlaya.orgLanguage: English - Date: 2014-07-22 12:59:12
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6![The 64th William Lowell Putnam Mathematical Competition Saturday, December 6, 2003 A–1 Let n be a fixed positive integer. How many ways are there to write n as a sum of positive integers, n = a1 + a2 + · · · + ak , The 64th William Lowell Putnam Mathematical Competition Saturday, December 6, 2003 A–1 Let n be a fixed positive integer. How many ways are there to write n as a sum of positive integers, n = a1 + a2 + · · · + ak ,](https://www.pdfsearch.io/img/23d25ee2f274512f0f30df670e0e3e72.jpg) | Add to Reading ListSource URL: kskedlaya.orgLanguage: English - Date: 2014-01-16 17:23:04
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7![The 62nd William Lowell Putnam Mathematical Competition Saturday, December 1, 2001 A–1 Consider a set S and a binary operation ∗, i.e., for each a, b ∈ S, a ∗ b ∈ S. Assume (a ∗ b) ∗ a = b for all a, b ∈ The 62nd William Lowell Putnam Mathematical Competition Saturday, December 1, 2001 A–1 Consider a set S and a binary operation ∗, i.e., for each a, b ∈ S, a ∗ b ∈ S. Assume (a ∗ b) ∗ a = b for all a, b ∈](https://www.pdfsearch.io/img/6a55377d4275ce2c9399c0e1bebb56e2.jpg) | Add to Reading ListSource URL: kskedlaya.orgLanguage: English - Date: 2014-01-16 17:22:58
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8![Solutions to the 73rd William Lowell Putnam Mathematical Competition Saturday, December 1, 2012 Kiran Kedlaya and Lenny Ng A–1 Without loss of generality, assume d1 ≤ d2 ≤ · · · ≤ d12 . 2 < d 2 + d 2 for some Solutions to the 73rd William Lowell Putnam Mathematical Competition Saturday, December 1, 2012 Kiran Kedlaya and Lenny Ng A–1 Without loss of generality, assume d1 ≤ d2 ≤ · · · ≤ d12 . 2 < d 2 + d 2 for some](https://www.pdfsearch.io/img/5785ccb9e76f94221a873123cb129e5a.jpg) | Add to Reading ListSource URL: kskedlaya.orgLanguage: English - Date: 2015-05-12 23:23:28
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9![The 66th William Lowell Putnam Mathematical Competition Saturday, December 3, 2005 A–1 Show that every positive integer is a sum of one or more numbers of the form 2r 3s , where r and s are nonnegative integers and no The 66th William Lowell Putnam Mathematical Competition Saturday, December 3, 2005 A–1 Show that every positive integer is a sum of one or more numbers of the form 2r 3s , where r and s are nonnegative integers and no](https://www.pdfsearch.io/img/e8c2e4dc94ff75234c7d83d05683acc0.jpg) | Add to Reading ListSource URL: kskedlaya.orgLanguage: English - Date: 2014-01-16 17:23:14
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10![The 61st William Lowell Putnam Mathematical Competition Saturday, December 2, 2000 A–1 Let A be a positive real number. What are the possible values of ∑∞j=0 x2j , given that x0 , x1 , . . . are positive numbers fo The 61st William Lowell Putnam Mathematical Competition Saturday, December 2, 2000 A–1 Let A be a positive real number. What are the possible values of ∑∞j=0 x2j , given that x0 , x1 , . . . are positive numbers fo](https://www.pdfsearch.io/img/d275c46786ffe22ef696cad72dcca2d3.jpg) | Add to Reading ListSource URL: kskedlaya.orgLanguage: English - Date: 2014-01-16 17:22:54
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