Candites

Logic Level 4

A candite is defined as a date $\text{DD/MM/YYYY}$ (that's right, not American) which contains consecutive digits in any order. An example of a candite is 23/06/1754 because it contains digits 0, 1, 2, 3, 4, 5, 6 and 7.

Find the first candite after the year 2015. If your answer can be represented as $\text{DD/MM/YYYY}$ , write your answer as $\overline{\text{DD}} \times \overline{\text{MM}} \times \overline{\text{YYYY}}$ .

The answer is 239190.

1 solution

Nihar Mahajan
May 21, 2015

Let the date be $D_1D_2/M_1M_2/Y_1Y_2Y_2Y_4$ .

Since we want the first candite after $2015$ , let $Y_1=2$ .
Since $2$ has already been used up , one of $D_i$ will be $0,1$ and one of $M_i$ will be $0,1$ .So we conclude that $Y_i \neq 0,1$ .
So we will take the least year possible , that is $Y_1Y_2Y_2Y_4=2345$ .
Since a month must be preferably earlier than the date , we have $M_1=0$ .
We see that $M_2 \neq 1$ because if its equal to $1$ then , $D_1D_2=67 , 76$ which is not possible.So to have least month we have $M_1M_2=06$ .
Similarly to have least date , we have $D_1D_2=17$ .
Thus the required product $=17\times 6 \times 2345 = \huge\boxed{239190}$

@Sharky Kesa @Pi Han Goh Is this the required date?

Nihar Mahajan - 6 years ago

Yeah, it is.

Sharky Kesa - 6 years ago

I am happy that I got it. :) .I suggest that you should have posted this problem on 17th June :P

Nihar Mahajan - 6 years ago

@Nihar Mahajan – Here's a follow-up question. Find all candites which do not contain the digit 0 in their month.

Sharky Kesa - 6 years ago

@Sharky Kesa – Let if possible that the month doesn't contain $0$ .Then compulsorily , $MM = 12$ and there will be only one possible solution $DD=30$ .Thus , the first possible date is $30/12/4567$ .

Nihar Mahajan - 6 years ago

@Nihar Mahajan – Next follow-up question. Prove that the year must not contain a 0.

Sharky Kesa - 6 years ago

@Sharky Kesa – Let if possible $0 \in YYYY$ .Then compulsorily $MM=12$ and there will be no existing and possible solution available for $DD$ which is a contradiction. Hence , the year must not contain a 0.

Nihar Mahajan - 6 years ago

Why do you need the comment "not American"?

Tran Hieu - 5 years, 5 months ago

Candites

The answer is 239190.

1 solution

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