Russell wanted to impress his coworkers. At a meeting, he announces that he can predict anyone's birthday if they tell him their birthday number. To get this famous birthday number, he asked everyone to do the following steps:

Take the month of your birthday (1 for January, 2 for February, etc.)
then multiply by 5
then add 7
then multiply it by 4
then add 13
then multiply by 5
then add the day of your birthday

Dave announced his birthday now was 612. Ricky said his was 1129 and Mike said his was 1436. Russell said "Well Dave, your birthday is April 7th. Ricky, yours is September 24th and Mike, you were born on the last day of the year, December 31st."

Make a conjecture about how Russell determines the birthday by examining the numbers.

How to solve this?


closed as off-topic by Gareth McCaughan, Alconja, M Oehm, Rosie F, IAmInPLS Oct 6 '16 at 9:58

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – Gareth McCaughan, Alconja, M Oehm, Rosie F, IAmInPLS
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  • 3
    $\begingroup$ Mathematics problem rather than puzzle. The "Make a conjecture" sounds to me like it's from a schoolteacher, so I reckon about 80% chance this is actually someone's mathematics homework. $\endgroup$ – Gareth McCaughan Oct 6 '16 at 9:34
  • $\begingroup$ That would be hilarious haha. $\endgroup$ – stack reader Oct 6 '16 at 13:17

You just need to reverse the process to get back the original values

x=month and y=day
I will use dave's info for the calculation
((x * 5 + 7) * 4 + 13) * 5 + y = 612
(20x + 41) * 5 + y = 612
100x + 205 + y = 612
100x + y = 407
we can now easily deduce that x is 4(April) and y is 7


Notice the pattern.

Get the month

Subtract two and get the month.
$612$ = 6 - 2 = 4 (April)
$1129$ = 11 -2 = 9 (September)
$1436$ = 14 -2 = 12 (December)

For the day

Subtract 5 and get the day.
$612$ = 12 - 5 = 7 (7th of April)
$1129$ = 29 - 5 = 24 (24th of September)
$1436$ = 36 - 5 = 31 (31st of December)

However there might some be rare cases where it might be difficult to use this. You'll have to see to that. In places where this doesn't work, you can reverse the equation and find it out by hand

I say rare because the calculations that Russell asks a person to do before giving the number makes it highly unlikely for such a case.

Either way you're covered :)


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