For example: If the answer chosen to question 3 is E, mark it this way on the question s column

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1 BS D Dear Participant, Shevat 5776 / February 206 Welcome to the 5776 International Ulpaniada Mathematics Competition. It is our pleasure to welcome you and all your fellow participants-girls from around the world who have risen to the challenge and are taking part in this unique event. We wish you all the very best! Fill in your details before you start answering the questions: Name: Grade level: address: Name of High School: CIty: Country/State: When you have completed the test, return to this page and enter your answers into the following table: For each question, mark an X on the answer you have chosen. For example: If the answer chosen to question is E, mark it this way on the question s column P.O.B. 6078, Bayit Vegan, Jerusalem 960, Israel Tel: , Fax: ulpaniadmacam.ail ulpaniada@macam.ail

2 This paper contains 4 questions. Each question shows five possible answers; only one is correct. Read each question carefully, solve it, and encircle the correct answer. You have 90 minutes to complete the test. You may use a calculator. B hatzlacha! How many squares are there in the following diagram? Enter 0 or into each square of the following 4X4 grid, such that the sum of numbers in any row, column, or main diagonal is 2. Some of the numbers have already been entered as shown. a b 0 What is the value of a+2b? 0 2 There isn t enough information. 2

3 The sum of four consecutive prime numbers is 272. The sum of the digits of the largest of these primes is: A plot is enclosed in a continuous fence which is built from segments of equal length, so that each segment is perpendicular to its neighboring segments (see diagram). If the area of the enclosed plot is 00 sq. metres, the length of the fence is: An L tromino is a piece made out of three squares of side, forming an L shape (see diagram). Five L trominos are placed together to form a new figur There are a few ways to do this. What is minimal perimeter of such a figure?

4 6 Consider the following cube of side with four of its face diagonals as shown in the figur What is the longest length a beetle can walk along the sides and face diagonals of the cube, without repeating any section twice? 2 8(+ 2) 2(+ 2) 2(6+ 2) 4(+ 2) 7 Each of the four questions in the following questionnaire has one correct answer. I. The correct answer to question II is: b a d c II. The correct answer to question III is: c d b a III. The correct answer to question IV is: d a c b IV. The correct answer to question I is: d c a b What is the correct answer to question III? a b c d There are a few possibilities. 4

5 8 The trapezoid ABCD contains two parallelograms ABED and AFCD (see illustration). AF and DE intersect at G. If the triangles AGD and FGE have the same area, then the ratio between the areas of the two trapezoids ABEG and ABCD is: 4/9 2/5 / /7 /8 9 Orit has three triangular pyramid shaped game tokens (as shown in the illustration). A different letter is written on each face of each pyramid, a total of 2 letters. Orit tossed the set of three tokens a total of eight times, and formed the following eight words from the three letters written on the pyramids bases after each toss: AND, DAY, NUT, FUR, BIN, BAN, ROT, OIL What are the three other letters on the pyramid containing the letter L? R,Y,N R,A,F N,R,U Y,D,U N,I,T 5

6 0 A six digit number is formed by using all the digits, 2,, 4, 5, 6. What is the probability that this number is divisible by? 0 / /720 /20 /24 The numerical value of התשע ו is =76 2. How many two digit numbers are there altogether, whose square ends with the two digit number itself? How many times can the number 5776 be obtained by starting from the 5 at the center of the table, and progressing in vertical, horizontal or diagonal moves?

7 In the following subtraction exercise, a,b,d,c,e are distinct odd digits, and f is the biggest possible even number which gives a right answer. a b c - d e f f f The value of a+b+c is: Three circles, each of radius are tangential to each other. A band is placed tightly around the circles, as shown in the diagram. The band s length is: 2 4π π π π Are you Done? Go back to the first page and mark your choices in the tabl Good luck! 7