Weekly Dose 9 - Maths Olympiad Practice

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The different triangular symbols represent different digits from 1 to 9. The symbols represent the same digits in both examples. Find the two-digit number represented by ? Solution: Rewrite the equations to: The rightmost The leftmost Answer: From the last digit in 3 rd row, we know From the right, From the left, Rewrite the equations to: From the right, compare and , From the left, the last digit for Rewrite the equations to:

Transcript of Weekly Dose 9 - Maths Olympiad Practice

Page 1: Weekly Dose 9 - Maths Olympiad Practice

The different triangular symbols represent different digits from 1 to 9. The symbols represent the same digits in both examples. Find the two-digit number represented by ?Solution:Rewrite the equations to:

The rightmost The leftmost

Answer:

From the last digit in 3rd row, we know From the right, From the left,

Rewrite the equations to:

From the right, compare and , From the left, the last digit for

Rewrite the equations to:

Page 2: Weekly Dose 9 - Maths Olympiad Practice

Three digit numbers such as 986, 852 and 741 have digits in decreasing order. But 342, 551, 622 are not in decreasing order. Each number in the following sequence is composed of three digits:100, 101, 102, 103, …, 997, 998, 999How many three digit numbers in the given sequence have digits in decreasing order?Solution:

From 0, 1, 2, … , 8, 9 these 10 digits, pick any three and rearrange it to form decreasing order.

Combination:

Answer:

Page 3: Weekly Dose 9 - Maths Olympiad Practice

Solution 1:

The time needed to fry 5 fishes (each fish has two sides) one at a time is minutes.Since 4 fishes can be fried at the same time, total time required can be reduced to minutes.

Let’s name each side of the fishes: . We can use the following method to fry the fishes in 15 minutes.

First 3-minutes ()Second 3-minutes ()Third 3-minutes ()Forth 3-minutes ()Fifth 3-minutes ()

Answer: minutes

It takes 6 minutes to fry each side of a fish in a frying pan. Only 4 fish can be fried at a time. What is the minimum number of minutes needed to fry 5 fish on both sides.

Page 4: Weekly Dose 9 - Maths Olympiad Practice

Solution:

For each potatoes collected, Jose need to walk the distance between the potato and the basket.

The total distance

Answer: seconds

A basket and 16 potatoes are placed in a straight line at equal intervals of 6 meters, with the basket fixed at the end. What is the shortest possible time for Jose to bring the potatoes one by one into the basket, if he starts from where the basket is and runs at an average speed of 3 meters per second?