Friday puzzle: zero to one hundred

Last week’s puzzle was where Lisa asks me some questions about my house number. The first thing to note is that since Lisa knows the number if she is told whether the first digit is a 3 or not, then I must have said that the number was less than 50 when I answered the first question (and since I lied, that means my house number is actually greater than 50). For the other two questions, there are four combinations, square and multiple of 4, square and not multiple of 4 etc. If you work out the numbers less than 50 that fall into each of these 4 groups then you’ll find the not-square groups are big; the square and multiple of 4 group contains 4,16,36 and the square not-multiple of 4 contains 1,9,25,49.

Now Lisa would not be able to say she knew the number if she knew whether the first digit was a 3 or not unless it is that first group (4,16,36) and if she herself lives at either 4 or 16 leaving only two remaining choices. This means that I must have said untruthfully that my number was a multiple of 4 and truthfully that my number was a square. So we know that in reality my number is greater than 50, not a multiple of 4 and a square. The squares greater than 50 are 64, 81 and 100 and only 81 is not a multiple of 4.

I live at number 81.

We’re all too tired after DAC to have a really challenging puzzle. This week’s puzzle is to look at the following list of the numbers from 0 to 100 and fill in the missing piece in the midde:

8 18 80 88 85 84 89 81 87 86 83 82 11 15 50 55 54 59 … 22 2 0

Answer next week

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