Chris Maslanka

Solutions

1 The Inland Revenue is not so draconian as to pass a company through a food processor, which was the incongruity this statement sparked. When we convert assets to cash to distribute to claimants we usually speak of liquidating them. [Point to Ponder: Is the use of “due to” correct in the example?] With thanks to Michael Kelly.

2 a) n = 8. b) [(√(2(√2)))]m = 2; so √2(√2) = 2(1/m), so 2(√2) = 2(2/m), and √2 = 2(½) = 2(2/m – 1); so (2/m – 1) = 1/2 and m = 4/3. [Point to Ponder: What if [(√2(√(2(√2))))]m = 2?]

3 The number, E, in the middle cell of a 3 X 3 magic square has to be a third of the magic number, M. To show this, sum along the 4 directions shown: (a + E + i) + (b + E + h) + (g + E + c) + (d + E + f ) = (a

+ b + c) + (d + E + f ) + (g + h + i) + 3E = 3M + 3E. But this equals 4M as we have summed the 3 cells along a row, a column and two diagonals; so 4M = 3M + 3E; so M

= 3E. But M = 9 + 1 + 8 = 18, whence the middle sum should be 18/3 = 6. But M then also equals 6 + 6 + 1 = 13 and 13 ≠ 18; so a contradiction: it is impossible.

4 Magnus Swottus turned the grid upside down, made a working magic square and turned it back upside down again. Upside down, it now works.

5 The central square of such a magic square must be the average of the numbers on either side of it. [How do you know?] Let the central cell contain 2n and those on either side be 2p and 2q; then [2p + 2q]/2 = 2n. Thinking in binary we need a number of the form 1,000 … plus another of the form 1, 000 … to equal another of the form 1,000 … This can only happen if the first and second have their solitary ones in the same place. The central one is double their sum divided by 2, so all three are the same. So only the trivial case is possible: all entries are the same (ie all of the form 2n). Wordplay: Wordpool c), a), d);

EPU CEREMONIAL; Dropouts

FRAILTIES; Word Centre

KEROSENE, MOROSELY, (XEROSERE); Cryptic BIFURCATE, POET, BALDERDASH; Missing Links

a) dock/leaf/mould b) bee/line/ dancing c) picture/perfect/pitch d) bug/bear/hug e) tower/block/ buster f) shooting/stars/truck