# INTERNATIONL MATHEMATICS AND SCIENCE OLYMPIAD FOR PRIMARY SCHOOLS (IMSO) 2006

Short Answer: there are 20 questions, fill in the correct answers in the answer sheet. Each correct answer is worth 2 points. Time limit: 60 minutes.

- What is the difference between 1+2+4+8+16+32+64+128+256+512+1024 and 2048?
- How many of the first twenty-five positive whole numbers can be expressed as the product of two different primes? (Note that 1 is not a prime.)
- How many times does the digit 9 appear in the answer when 1010101 is subtracted from 1000000000000?
- In a triangle the length of one side is 3.8 cm and the length of another side is 0.6 cm. We know that the length of the third side, when expressed in centimeters, is an integer. Find the length.

# Primary Mathematics World Contest Problems for Team Contest

T1. Candle A, one centimeter longer than Candle B, was lit at 5:30 p.m. and Candle B was lit at 7:00 p.m. Each candle burns at a constant rate. At 9:30 p.m, the two candles were of the same length. Candle A burned out at 11:30 p.m. while Candle B burned out at 11:00 p.m. How many cm was Candle A before it was lit?

T2. What is the time on a clock between 4 o’clock and 5 o’clock, if the minute hand and the hour hand are overlapping each other?

T3. What is the largest number of consecutive positive integers that add up to exactly 1000?

T4. How many different paths are there that begin with “M” and end with “S” to spell the word “MATHS” in this picture?

# Mathematics Exploration Problems (IMSO 2005)

International **Mathematics and Science Olympiad** (IMSO) for Primary School 2005

1. The following figure shows a road map of the Gotthem City. Every road is one way, as indicated by the arrow.

Questions:

(a) [1 point] How many possible routes are there from A to D?

(b) [2 points] How many possible routes are there from A to H?

(c) [3 points] How many possible routes are there from A to L?

2. There are some people playing a card game. On the table there are fifty cards, numbered 1 to 50, all facing up. Each player is allowed to choose a certain number of cards. If the sum of the numbers on all the cards chosen by the player is the highest, then he/she is the winner. There is only one winner.

Questions:

What is the lowest possible score that makes a player a sure winner if each player has

to choose:

(a) [2 points] two cards?

(b) [2 points] three cards?

(c) [2 points] five cards?

# International Mathematics and Science Olympiad (IMSO) for Primary School 2005

I have found Mathematics Exploration Problems in my folder. Please solve this problems correclty.

1. The following figure shows a road map of the Gotthem City. Every road is one way, as indicated by the arrow.

Questions:

(a) [1 point] How many possible routes are there from A to D?

(b) [2 points] How many possible routes are there from A to H?

(c) [3 points] How many possible routes are there from A to L?

2. There are some people playing a card game. On the table there are fifty cards, numbered 1 to 50, all facing up. Each player is allowed to choose a certain number of cards. If the sum of the numbers on all the cards chosen by the player is the highest, then he/she is the winner. There is only one winner. Questions:

What is the lowest possible score that makes a player a sure winner if each player has to choose:

(a) [2 points] two cards?

(b) [2 points] three cards?

(c) [2 points] five cards?

# INTERNATIONL MATHEMATICS AND SCIENCE OLYMPIAD FOR PRIMARY SCHOOLS (IMSO) 2006

INTERNATIONL MATHEMATICS AND SCIENCE OLYMPIAD FOR PRIMARY SCHOOLS (IMSO) 2006. Mathematics Contest in Taiwan, Exploration Problems.

Answer the following 5 questions, and show your detailed solution in the answer sheet. Write down the question number in each paper. Each question is worth 8 points. Time limit: 60 minutes.

1. The solution to each clue of this crossnumber is a two-digit number. None of

these numbers begins with zero. Complete the crossnumber, stating the order in which you solved the clues and explaining why there is only one solution.

Clues Across

1. A square number

3. A multiple of 11

Clues Down

1. A multiple of 7

2. A cube number

2. Notice that 2^2 + 2^2 = 2^3 , so two squares can sum to give a cube; however, the two squares here are equal (to 4).

(a) Find two unequal squares whose sum is a cube.

(b) Show that there are infinitely many pairs of unequal squares whose sum is

equal to a cube.