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Calendar Patterns

Stage: 2 Challenge Level: Challenge Level:1

Anil (Irmak Primary School, Turkey) explored some adding patterns:

$1 + 8 = 9$
$2 + 9 = 11$
$3 + 10 = 13$
$4 + 11 = 15$
$5 + 12 = 17$
$6 + 13 = 19$
$7 + 14 = 21$
$8 + 15 = 23$

Alice from Perse School for Girls spotted a pattern:


There is a pattern, it's that the two numbers diagonal to each other added together make the same number as the other pair of diagonal numbers make.

Chris found another pattern using multiplication:

If you cross multiply the set of four numbers, their difference is always $7$.
$1 \times 9 = 9$ and $2 \times 8 = 16$, difference $= 7$
$3 \times 11 = 33$ and $4 \times 10 = 40$, difference $= 7$
$15 \times 23 = 345$ and $16 \times 22 = 352$, difference $= 7$ etc...

If you discovered any other patterns, then do let us know. Please don't worry that your solution is not "complete" - we'd like to hear about anything you have tried.