Powerball fever hit the Curious office last week like a tornado. I don't think anyone actually bought any tickets, but we debated whether to take the lump sum or the annuity payment with passion best described as "grossly unnecessary".
As we all know, winning Powerball requires picking some special numbers. And Henry loves a particular special two-digit number where when you add the sum of the digits to the product of the digits, you get the original number. His special number is the smallest two-digit number that has this cool (and nerdy) property.
What's Henry's special number?
Ready for the answer?
OK, if you did this one all the way through, you found something amazing...
While winning the Powerball lottery is nearly impossible, this one is easy with a little algebra. Let a = the 10s digit and b = the 1s digit. So we're looking for the smallest number where:
Actually, that's right. Any two-digit number that ends in 9 has this property.
While winning the Powerball lottery is nearly impossible, this one is easy with a little algebra. Let a = the 10s digit and b = the 1s digit. So we're looking for the smallest number where:
- a + b + a*b = 10a + b
- a*b = 9a
- b = 9
Actually, that's right. Any two-digit number that ends in 9 has this property.
- 1 + 9 + 1*9 = 10 + 9 = 19
- 2 + 9 + 2*9 = 11 + 18 = 29
- 3 + 9 + 3*9 = 12 + 27 = 39
- 4 + 9 + 4*9 = 13 + 36 = 49
- 5 + 9 + 5*9 = 14 + 45 = 59
- 6 + 9 + 6*9 = 15 + 54 = 69
- 7 + 9 + 7*9 = 16 + 63 = 79
- 8 + 9 + 8*9 = 17 + 72 = 89
- 9 + 9 + 9*9 = 18 + 81 = 99
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