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If you take the number 24 and remove the units digit (4), 2 remains, and 24 is divisible by 2. Such a number, which happens to be divisible by itself truncated by its units digit is called a “trucadivisible” number. How many “trucadivisible” numbers less than 1995 are there?

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sqdancefan

Answer:

  222

Step-by-step explanation:

The "truncadivisible" numbers include ...

  • all 10 numbers 10-19
  • 5 even numbers 20-28
  • 4 numbers divisible by 3 in [30, 39]
  • 3 numbers divisible by 4 in [40, 48]
  • 2 numbers divisible by their tens digit in each decade [50, 99], for a total of 10 numbers

So far, we have 32 numbers less than 100.

In the range [100, 1995], only numbers divisible by 10 are "truncadivisible." There are 190 of those.

In total, 222 numbers in the range [1, 1995] are "truncadivisible."