1 out of 3
Find the five distinct digits N, R, I, C and H in the following nomogram
1 out of 3
Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). The question asks you to explain the trick.
2 out of 3
If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.
2 out of 3
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
3 out of 3
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
3 out of 3
What is the sum of all the digits in all the integers from one to one million?
3 out of 3
Can you explain what's happening with these numbers?
3 out of 3
Explore the factors of the numbers which are written as 10101 in different number bases. Prove that the numbers 10201, 11011 and 10101 are composite in any base.
3 out of 3
A composite number is one that is neither prime nor 1. Show that 10201 is composite in any base.
2 out of 3
If the last four digits of my phone number are placed in front of the remaining three you get one more than twice my number! What is it?
