Hi, me and Cody had found a solution and it has a 9/10 chance of working each round. the solution makes you figure out the randomly generated number in just 2 questions.
The method is that first time you divide by 10 and the seccond time you devide by 9.here is an example: number:???
My number divided by 10 has an remainder of 6
My number divided by 9 has an remainder of 5
in this case you know that the number is going to end in a 6 as it devided by has a remainder of 6. The next step is that you add the remainder amount onto the 9 (in this case 9 + 5 = 14)and see if it ends in 6. If it doesn't, just go 2 x 9 + the remainder (in this case 2 x 9 + 5 = 23). If it still doesn't work then just go 3 x 9 + the remainder and so on until you find a number that ends in a 6 (Note the 6 is just an example here as it is the remainder of the number devided by 10).In this case it would be 9 x 9 + 5 = 86 so 86 will be the answer. There are only two types of questions that this method would not work on.
Question 1:
My number divided by 10 has an remainder of 2
My number divided by 9 has an remainder of 2
In this case, the number ends in a 2 because the number devided by 10 gives you a remainder of 2 however the number devided by 9 also gives you a remainder of 2. In this case there are 2 possible choices: 2 or 92. The number 2 doesn't go into 9 or 10 so it stays as it is while 92 divided by 10 gives a remainder of 2 and 92 divided by 9 gives a remainder of 2. There are no other possible choices. Right now you have 2 choices of either guessing between the 2 as you have a 1/2 chance or just ask another question.If you face this question it will be the remainder of the number devided by 10 or 90 + the remainder of the number devided by 10.
Question 2:
My number divided by 10 has an remainder of 9
My number divided by 9 has an remainder of 0
In this case, the number ends in a 9 because the number devided by 10 gives you a remainder of 9 however the number can go into 9 without remainders so again there are 2 posssible answers : 9 or 99. Both off these numbers go into 10 with an remainder of 9 and both of these numbers go into 9 without remainders. So in this question, agaain you ether make a guess or ask another question.
Other then these 2 types of tquestions this method works perfectly. Here is a photo with the circles labled 1 - 100 just show show better how it works.