Missing-Figure Problems

Extract

In a recent number of the Mathematical Gazette (March 1920) I proposed the following problem for solution:

Some of the figures in the long division sum have been replaced by crosses, and it is required to restore them. Four solutions are possible—of course in scale ten. It is understood that the sum is to be worked as in elementary arithmetic and that there is nothing fictitious. There must be no line of zeros, neither must the left-hand figure of any line be zero. In the divisor the digits figure ought not to be zero (for such a zero would ordinarily be cancelled before working the sum), but it is not enough to assume this: proof must be possible from the data. In the Four Fours the proof is instantaneous, because there is no remainder and the right-hand figure of the dividend is 4.