Hard Math

I remember some math questions from the math Olympiads, so can you do better than I can? Good luck!

1) a-squared +b-squared=2018-2a, what is a and b?

2) What is the last non-0 digit of 50!

3a) a and b are positive integers, where a= the sum of all the digits of a and b, and b= the product of all the digits of a and b. Find all pairs that satisfy this equation, under 100.

3b) FInd all pairs under 1000, and one of the numbers has to be over 99.

Really, I only got an answer for 2 (probably wrong), and nothing for the rest. Please tell me what you got, and please note, I might have remembered this wrong. But, it should still be right. How did you go? :)

Note by Caleb Kum
2 weeks, 2 days ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

Q1) The answer is that there are no possible INTEGRAL a and b satisfying the equation..................otherwise there are infinitely many pairs of a and b..........

Aaghaz Mahajan - 2 weeks ago

Log in to reply

What I found that it may seem like that, but when I did it, it would always be short. So, (Idk if this is right) there should be only one answer.

Caleb Kum - 2 weeks ago

Log in to reply

I rechecked my calculations and found no error..........Check again..........There are no Integral a and b satisfying the condition...........If you have found a solution, then tell me the answer....... :)

Aaghaz Mahajan - 2 weeks ago

Log in to reply

@Aaghaz Mahajan Ok, I'll take your word for it. Hey, anyone, can YOU find an answer? (I can't be stuffed to do so).

Caleb Kum - 2 weeks ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...