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The Number Blocks

 The children in the illustration have found that a large number of very interesting and instructive puzzles may be made out of number blocks; that is, blocks bearing the ten digits or Arabic figures—1, 2, 3, 4, 5, 6, 7, 8, 9, and 0.  The particular puzzle that they have been amusing themselves with is to divide the blocks into two groups of five, and then so arrange them in the form of two multiplication sums that one product shall be the same as the other.  The number of possible solutions is very considerable, but they have hit on that arrangement that gives the smallest possible product. Thus, 3,485 multiplied by 2 is 6,970, and 6,970 multiplied by 1 is the same.  You will find it quite impossible to get any smaller result. Now, my puzzle is to find the largest possible result.  Divide the blocks into any two groups of five that you like, and arrange them to form two multiplication sums that shall produce the same product and the largest amount possible.  That is all, and yet it is a nut that requires some cracking.  Of course, fractions are not allowed, nor any tricks whatever.  The puzzle is quite interesting enough in the simple form in which I have given it.  Perhaps it should be added that the multipliers may contain two figures. See answer

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