An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Choose any three by three square of dates on a calendar page...
Can you create a Latin Square from multiples of a six digit number?
Consider numbers whose first digit is 1. Looking at each possible value for the second digit we find 9 such numbers.
110, 121, 132, 143, 154, 165, 176, 187, 198.
Similarly there are 8 numbers starting with 2; 7 numbers starting with 3...
Lastly there is only one number starting with 9: 990.
Hence the total is 9+8+7+6+5+4+3+2+1 = 45.
This problem is taken from the UKMT Mathematical Challenges.