000RM.dvi

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18.Find a number of the formab 0 cdwhose square contains the nine

digits 1, 2, 3, 4, 5, 6, 7, 8, 9.^13

19.Find a perfect cube whose digits form a permutation of consecutive

digits. (See also E538).^14

20.Find a square of ten digits such that the two numbers formed by the

first five and last five digits are consecutive.^15

21.Find the smallest four-digit number such that the sum of products

of pairs of digits is equal to the sum of products of sets of three.

22.Find three three-digit numbers in geometrical progression which

can be derived from one another by cyclic permutation of digits.

(See also E714).

(^13) The squares: 326597184,361874529,529874361,576432081,627953481,842973156.
14. = 8365427^3203 The only higher powers satisfying the same condition are the fifth powers of 32 and
243.
15. = 4049540496^2 = 1322413225; 63636^236365