Sum modulo 12 and divisor of 4

Find the modulo 7 of the modulo 12 plus its divisor of 4

Level selection

How to play— show the rules

To build speed and confidence in your date-to-weekday conversions, it is essential to practise combining the steps of the doomsday algorithm quickly.

In this game you will practise finding the sum of two numbers and taking modulo 7 of the result.

The first number is the modulo 12 of the last two digits of the year. If you haven’t already, you should first be confident in the Modulo 12 game.

The second number is the divisor of 4 of the number above — that is, how many whole 4s fit into it. See the Divisor of 4 game to practise this operation.

Finally, take the sum of these two numbers and find its modulo 7. That is your answer for the round.

Here are some examples:

1904

04 % 12 = 4

⌊⁴/₄⌋ = 1

(4 + 1) % 7 = 5

1913

13 % 12 = 1

⌊¹/₄⌋ = 0

(1 + 0) % 7 = 1

1935

35 % 12 = 11

⌊¹¹/₄⌋ = 2

(11 + 2) % 7 = 6

1966

66 % 12 = 6

⌊⁶/₄⌋ = 1

(6 + 1) % 7 = 0

1991

91 % 12 = 7

⌊⁷/₄⌋ = 1

(7 + 1) % 7 = 1

2027

27 % 12 = 3

⌊³/₄⌋ = 0

(3 + 0) % 7 = 3