3
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From Dante's Infernal Puzzle Collection:

Excessive thrift, I learned, may be a sin, when love of wealth does triumph over all, and man forgets his duties to his Lord. In that dark place a preacher grey I found, clutching to himself a chest of slates. In broken words, he told me of the way in which he'd clutched to himself every bit.

Within his chest he carried here with him the numbered slates that he had used in life to indicate to those within his church the numbered hymns for the service there. From one to eight hundred these hymns ran, and four of them were called for each day's prayer. The preacher swelled with pride to let me know that he had just the minimum of slates required to satisfy each day's new need. He even bragged how 'six' could serve as 'nine', by simple means of rotation of slates.

So tell me now, how many slates had he, clutched there to his bosom in that chest?

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5
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Here are the maximum numbers of each digit the preacher might need, with examples of configurations that use those digits:

0: 8, like in 100 200 300 400
1: 9, like in 111 211 311 411
2: 9, like in 122 222 322 422
3: 9, like in 133 233 333 433
4: 9, like in 144 244 344 444
5: 9, like in 155 255 355 555
7: 9, like in 177 277 377 777
8: 8, like in 188 288 388 488
6/9: 12, like in 666 669 696 699

Summing up all the numbers of each slate necessary (the bolded numbers) gives a final answer of:

82 slates.

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  • 1
    $\begingroup$ Well done, and thank you for providing reasons WHY you would need x amount of slates per number! $\endgroup$ – Josh Jun 3 '17 at 20:02

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