Maths Society

# PBΔG Problems

### Welcome to our problems page.

##### This Week’s Question:

What is the remainder of:
x9 + 7x8 + 5x7 – 9x6 + 12x5 – 19x4 – 11x3 – 18x2 + 20x + 12 x+1

-14

##### Past Questions And Answers:

Can you work out what was eaten each day based on these clues?
1. The salad starter was eaten on Tuesday, which was earlier in the week than the trifle dessert
2. The prawn starter and apple pie were eaten in the same meal, the evening before the mushroom starter and steak main
3. The ice cream was the evening before the curry (which was not served on a tuesday)
4. The tomato soup and the chicken were served on the same day

Evening Starter Main Dessert
Monday Soup Chicken Cake
Tuesday Salad Fish Ice Cream
Wednesday Prawn Curry Apple Pie
Thursday Mushroon Steak Trifle

3x + 4y – z = 0
x – 3y + 4z = 26
– 4x + y + 4z = -14

What are x, y and z?

x = 5
y = -3
z = 3

What is the probability that within a group of 23 people, at least 2 of them share a birthday?

~50%

24x2 + 25x – 47 ax – 2 = – 8x – 3 –53ax – 2
for x ≠ 2a
What is the value of a?

a = -3
A group of 100 students took a maths paper with 4 questions:
90 people got the first question correct
85 people got the second question correct
80 people got the third question correct
75 people got the last question correct
What is the minimum number of people to get all four questions correct?

30
🏠 🏠 🏠
🔥 💧 ⚡
Is it possible to join each house to each utility?
What are the conditions for it to be solved?

This puzzle is not possible in 2D. However it is possible on a surface topologically similar to a torus (eg a mug) where there is a hole for a line to pass through. Watch linked video for some solutions
If 9999 = 4
8888 = 8
1816 = 6
1212 = 0

What is 1919 = ?

4
(number of closed areas) x (number of unclosed numbers)
At an office party, everyone shook hands with everyone else. There were a total of 66 handshakes.
How many people were at the party?

12
What is the difference between 10% of one million and 10% of one thousand?

99900
What is the final digit of 2^1000?

6
If:
10 + 10 = 20
6 + 6 = 10
14 + 8 = 20

What is 8 + 13?

1B
Everything is in base 12
All 3 digit positive integers whose digit sum is 5 are listed in ascending order.
What is the median of the list?

221
Using only addition, how can you add eight 8s to get the number 1000?

888 + 88 + 8 + 8 + 8

It takes 1629 digits to number the pages of a document.
How many pages does the book have?

579
What is the difference between the sum of the first 2018 even numbers and the sum of the first 2018 odd numbers?

2018
5🔺6 = 30111
8🔺2 = 16106
9🔺4 = 36135

What is 7🔺3?

21104
Can you order all 9 digits so that the first 2 are a multiple of 2, the first 3 are a multiple of 3 and so on all the way up to 9 digits?

Yes: 381,654,729
What is unique about the number 8549176320?

The digits are in alphabetical order
If function ♢ is defined as x♢y = x^y-y^x
What Is (2♢3)♢4?

3/4