The Sunday Times Teasers Book 1: Challenge yourself with 100 lateral-thinking puzzles (The Sunday Times Puzzle Books)

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So if the length of wire is between these values, we can link the cells in the 13×13 grid, but not the 14×14 grid. We have encountered similar puzzles before. (See: Enigma 1154, Enigma 1194, Enigma 228, Enigma 221, Enigma 122, Enigma 1635). How many patients come with complaints about one part of their anatomy (ears or nose or throat) only? Of his 60 patients, the number complaining of ears and nose only is three times as great as the number complaining of ears and throat only. Bo then chooses to discard the 10 of Diamonds, and is dealt 4 of Hearts (the card discarded by Jo):

I used the [[ Matrix.linear() ]] solver from the enigma.py library to find assignments that give non-negative points values. (Although there are no further solutions if negative values are permitted).

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This Python program looks for sets of 4 or 9 numbers from 1 to 10 whose squares sum to a square number. We then choose 5 of these sets to form the different types of muesli made, and look for the 2 (different) unavailable ingredients. The first unavailable ingredient only allows 2 of the types to be made (these are “basic” and “fruity”) and the second only allows 1 to be made (and this is “luxury”).

My answer to the originally posted puzzle (with an upper limit of “less than 15 cm”) was the same, and is as follows: Although the program looks for “reasonable” solutions, it is possible there may be a line with more than 6 connections that is not found by the program). products {476, 486, 936, 1044, 1296, 1394, 1638, 1827, 1988, 2187, 5822, 5832}, 2 rearrangements [7 others] If we use variables A, B, C, D, E to correspond to the points allocated (according to mothers name), then we can allocate the first names and surnames of the cubs to the same set of variables to give us a set of simultaneous linear equations, which we can attempt to solve to give the points values. The [[ Delay() ]] class from the enigma.py library is used to calculate the digits and prime factors of the age only as necessary. (Although in the event this doesn’t save a great deal of processing).

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From these we can construct many viable arrangement of letters. For example: E A J D G F L R U I N Y.

In the revised puzzle, only the 13×13 grid is considered, so this must provide the answer. (Which makes me wonder why the puzzle has all the stuff about straightening the paperclip at all). I assumed each mixture has multiple ingredients, and as there are only 10 possible ingredients this means each must have 4 or 9.This Python program finds maximal groups of birthdays sharing day-of-month and day-of-week for academic years starting in the 1980s, and then looks for maximal groups satisfying the remaining conditions. So the youngest two are Mike and Ken (= 13 points in total), and Ivan must be Ken’s best friend (= 10 points in total). If φ is the Golden Ratio, then: y = φ − 1 = 1/φ, but we don’t need to deal with the actual value of y, instead we note: The 12 points fall into two regular hexagonal orbits, and once the initial letter is selected we must stay in that particular orbit, making transitions of ±1 or 3 to move between letters. Therefore any word spelled out must not have more than 6 different letters (which eliminates 4 of the days of the week, and 3 months of the year). It’s all very confusing, I know; but I can tell you that there are 110 complaints in all — if you count a complaint about two ears as one complaint.

It wasn’t clear to me if 0 digits were allowed or not, or if repeated digits were allowed, so I wrote code to solve the most permissive interpretation. But it turns out there is the same unique answer whatever variation is used. The first (13×13) grid needs a wire of around 11.3 cm in length to link the cells, and the second (14×14) grid needs a wire of around 14 cm to link the cells. For each case simultaneous linear diophantine equations can be formed in appropriate unknowns N(a) N(b) etc to give sums 37, 39, 41 .

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The unavailable ingredient this week is 10, meaning only (2, 4, 5, 6) can be made, and this is “luxury”.