Puzzles
24 December
The digital product of a number is computed by multiplying together all of its digits.
For example, the digital product of 1522 is 20.
How many 12-digit numbers are there whose digital product is 20?
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20 can be written as the product of one-digit numbers greater than 1 in the following ways:
Our 12-digit numbers must contain one of these plus lots of 1s.
In the first case, there are 12×11=132 different possible positions for the 4 and the 5.
In the second case, there are 12×11×10×½=660 different possible positions for the 2s and the 5.
In total, this makes 132+660=792 numbers.
17 December
The digital product of a number is computed by multiplying together all of its digits.
For example, the digital product of 6273 is 252.
Today's number is the smallest number whose digital product is 252.
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252 can be written as the product of one-digit numbers in the following ways:
- 2×2×3×3×7
- 2×2×9×7
- 2×3×6×7
- 3×3×4×7
- 6×6×7
- 4×9×7
Therfore, the smallest number whose digital product is 252 is 479.
