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Can't You Do Division? by Oyler

L4438

Can't You Do Division? by Oyler

In February 1967, The Listener published puzzle number 1916, Can You Do Division? by Rhombus. This puzzle uses the same grid and lettering as the original. The clues give the number of factors of the answer (including 1 and itself). Furthermore, each row and column contains all of the digits from 1 to 9 inclusive. The four entries around the perimeter are perfect squares to be deduced. All grid entries are different. Capital letters denote across entries and lower case denote down entries.

The factors of a number are the products of the different combinations of zero or more of each of its prime factors. Thus the number of factors is the product of (1 + the number of occurrences of x) for each distinct prime factor x. For example, 54 = 2333, its factors are {1, 2, 3, 23, 33, 233, 333, 2333} and the number of factors is (1+1)(1+3) = 8.