Pi School

Pi School The Pi School is an after school program that offers curricular and extra curricular enriched course

Problem (Preparation for Waterloo Math Contests)[AHSME 1976]: If ​\( \, p\, \)​ and ​\( \, q\, \)​ are primes and ​\( \,...
03/14/2025

Problem (Preparation for Waterloo Math Contests)[AHSME 1976]: If ​\( \, p\, \)​ and ​\( \, q\, \)​ are primes and ​\( \, x^2 -px +q=0\, \)​ has distinct positive integral roots, find ​\( \, p\, \)​ and ​\( \, q. \)​...

Problem (Preparation for Waterloo Math Contests)[AHSME 1976]: If ​\( \, p\, \)​ and ​\( \, q\, \)​ are primes and ​\( \, x^2 -px +q=0\, \)​ has distinct positive integral roots, find ​\( \, p\, \)​…

Problem (Preparation for Waterloo Math Contests): Find all positive integers ​\( \, n\, \)​ for which ​\( \, 3n -4, \,\,...
03/11/2025

Problem (Preparation for Waterloo Math Contests): Find all positive integers ​\( \, n\, \)​ for which ​\( \, 3n -4, \,\, 4n - 5, \,\, \mbox{and}\, \,\, 5n-3\, \)​ are all prime numbers....

Problem (Preparation for Waterloo Math Contests): Find all positive integers ​\( \, n\, \)​ for which ​\( \, 3n -4, \,\, 4n – 5, \,\, \mbox{and}\, \,\, 5n-3\, \)​ are all prime numbers.…

Problem (Preparation for Waterloo Math Contests): A bug moves in the coordinate plane, starting at (0,0). On the first t...
03/07/2025

Problem (Preparation for Waterloo Math Contests): A bug moves in the coordinate plane, starting at (0,0). On the first turn, the bug moves one unit up, down, left, or right, each with equal probability. On subsequent turns the bug moves one unit up, down, left, or right, choosing with equal probability among the three directions other than that of its previous move. For example, if the first move was one unit up then the second move has to be either one unit down or one unit left or one unit right. After four moves, what is the probability that the bug is at (2,2)?...

Problem (Preparation for Waterloo Math Contests): A bug moves in the coordinate plane, starting at (0,0). On the first turn, the bug moves one unit up, down, left, or right, each with equal probabi…

Problem (Preparation for Waterloo Math Contests): A point with coordinates (a,2a) lies in the 3rd quadrant and on the cu...
03/05/2025

Problem (Preparation for Waterloo Math Contests): A point with coordinates (a,2a) lies in the 3rd quadrant and on the curve given by the equation 3x2 + y2 = 28. Find a....

Problem (Preparation for Waterloo Math Contests): A point with coordinates (a,2a) lies in the 3rd quadrant and on the curve given by the equation 3×2 + y2 = 28. Find a.

Problem (Preparation for Waterloo Math Contests): Centuries ago, the pirate Captain Blackboard buried a vast amount of t...
01/13/2025

Problem (Preparation for Waterloo Math Contests): Centuries ago, the pirate Captain Blackboard buried a vast amount of treasure in a single cell of a 2 × 4 grid-structured island. You and your crew have reached the island and have brought special treasure detectors to find the cell with the treasure. For each detector, you can set it up to scan a specific subgrid [a, b]×[c, d] with 1 ≤ a ≤ b ≤ 2 and 1 ≤ c ≤ d ≤ 4. Running the detector will tell you whether the treasure is in the region or not, though it cannot say where in the region the treasure was detected. You plan on setting up Q detectors, which may only be run simultaneously after all Q detectors are ready. What is the minimum Q required to guarantee your crew can determine the location of Blackboard’s legendary treasure?...

Problem (Preparation for Waterloo Math Contests): Centuries ago, the pirate Captain Blackboard buried a vast amount of treasure in a single cell of a 2 × 4 grid-structured island. You and your crew…

Problem (Preparation for Waterloo Math Contests): A bug moves in the coordinate plane, starting at (0,0). On the first t...
01/08/2025

Problem (Preparation for Waterloo Math Contests): A bug moves in the coordinate plane, starting at (0,0). On the first turn, the bug moves one unit up, down, left, or right, each with equal probability. On subsequent turns the bug moves one unit up, down, left, or right, choosing with equal probability among the three directions other than that of its previous move. For example, if the first move was one unit up then the second move has to be either one unit down or one unit left or one unit right....

Problem (Preparation for Waterloo Math Contests): A bug moves in the coordinate plane, starting at (0,0). On the first turn, the bug moves one unit up, down, left, or right, each with equal probabi…

Problem (Preparation for Waterloo Math Contests): A number n has sum of digits 100, whilst 44n has sum of digits 800. Fi...
11/27/2024

Problem (Preparation for Waterloo Math Contests): A number n has sum of digits 100, whilst 44n has sum of digits 800. Find the sum of the digits of 3n....

Problem (Preparation for Waterloo Math Contests): A number n has sum of digits 100, whilst 44n has sum of digits 800. Find the sum of the digits of 3n.

Problem (Preparation for Waterloo Math Contests): Are there more positive integers under a million for which the nearest...
11/19/2024

Problem (Preparation for Waterloo Math Contests): Are there more positive integers under a million for which the nearest square is odd or for which it is even?...

Problem (Preparation for Waterloo Math Contests): Are there more positive integers under a million for which the nearest square is odd or for which it is even?

Problem (Preparation for Waterloo Math Contest): Some pairs of towns are connected by a road. At least 3 roads leave eac...
11/14/2024

Problem (Preparation for Waterloo Math Contest): Some pairs of towns are connected by a road. At least 3 roads leave each town. Show that there is a cycle containing a number of towns which is not a multiple of 3....

Problem (Preparation for Waterloo Math Contest): Some pairs of towns are connected by a road. At least 3 roads leave each town. Show that there is a cycle containing a number of towns which is not …

Problem: A chooses a positive integer X ≤ 100. B has to find it. B is allowed to ask 7 questions of the form "What is th...
11/11/2024

Problem: A chooses a positive integer X ≤ 100. B has to find it. B is allowed to ask 7 questions of the form "What is the greatest common divisor of X + m and n?" for positive integers m, n < 100. Show that he can find X....

Problem: A chooses a positive integer X ≤ 100. B has to find it. B is allowed to ask 7 questions of the form “What is the greatest common divisor of X + m and n?” for positive integers …

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1371 Neilson Road
Toronto, ON
M1B4Z8

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Tuesday 9am - 5pm
Wednesday 9am - 5pm
Thursday 9am - 5pm
Friday 9am - 5pm
Saturday 9am - 5pm
Sunday 9am - 5pm

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+14167242243

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