I think you can do it with 6.72 on average. Start with the above 50 question, then split again with the above 25 question. Now, if it less than 25, 'ask is it 16 or under?'. If it is then it takes 4 more guesses (2^4=16). If it is above you have 9 possibilities. 7 of these take 3 guesses (for example 'if it is less than or equal to 20?' and we know it is more than 16, then that's 2 more guesses, so 3 in total). And 2 of them take 4 guesses (for example, 'is it greater than 23', still leaves 23 and 24).

We then do the same for the branches between 26 and 50, 51 and 75 and 76 and 100.

So to sum up, we have 6 * 16 * 4+5 * 7 * 4+7 * 2 * 4 all divided by 100 gives 6.72 questions on average.

I think you can do it with 6.72 on average. Start with the above 50 question, then split again with the above 25 question. Now, if it less than 25, 'ask is it 16 or under?'. If it is then it takes 4 more guesses (2^4=16). If it is above you have 9 possibilities. 7 of these take 3 guesses (for example 'if it is less than or equal to 20?' and we know it is more than 16, then that's 2 more guesses, so 3 in total). And 2 of them take 4 guesses (for example, 'is it greater than 23', still leaves 23 and 24).

We then do the same for the branches between 26 and 50, 51 and 75 and 76 and 100.

So to sum up, we have 7 * 16 * 4+ 6 * 7 * 4+ 7 * 2 * 4 all divided by 100 gives 6.72 questions on average.

I think you can do it with 6.72 on average. Start with the above 50 question, then split again with the above 25 question. Now, if it less than 25, 'ask is it 16 or under?'. If it is then it takes 4 more guesses (2^4=16). If it is above you have 9 possibilities. 7 of these take 3 guesses (for example 'if it is less than or equal to 20?' and we know it is more than 16, then that's 2 more guesses, so 3 in total). And 2 of them take 4 guesses (for example, 'is it greater than 23', still leaves 23 and 24).

We then do the same for the branches between 26 and 50, 51 and 75 and 76 and 100.

So to sum up, we have 6164+574+724 all divided by 100 gives 6.72 questions on average.

I think you can do it with 6.72 on average. Start with the above 50 question, then split again with the above 25 question. Now, if it less than 25, 'ask is it 16 or under?'. If it is then it takes 4 more guesses (2^4=16). If it is above you have 9 possibilities. 7 of these take 3 guesses (for example 'if it is less than or equal to 20?' and we know it is more than 16, then that's 2 more guesses, so 3 in total). And 2 of them take 4 guesses (for example, 'is it greater than 23', still leaves 23 and 24).

We then do the same for the branches between 26 and 50, 51 and 75 and 76 and 100.

So to sum up, we have 6 * 16 * 4+5 * 7 * 4+7 * 2 * 4 all divided by 100 gives 6.72 questions on average.