The 𝚌a𝚕𝚎𝚗𝚍𝚊𝚛 𝚘𝚏 𝚝𝚑𝚎 𝚢𝚎𝚊𝚛 2024 𝚒𝚜 𝚝𝚑𝚎 𝚜𝚊𝚖𝚎 𝚏𝚘𝚛 𝙰.2044 𝙱.2032 𝙲.2040 𝙳.2036


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Question Number 208876 by Tawa11 last updated on 26/Jun/24

The 𝚌a𝚕𝚎𝚗𝚍𝚊𝚛 𝚘𝚏 𝚝𝚑𝚎 𝚢𝚎𝚊𝚛 2024 𝚒𝚜 𝚝𝚑𝚎 𝚜𝚊𝚖𝚎 𝚏𝚘𝚛 𝙰.2044 𝙱.2032 𝙲.2040 𝙳.2036
Commented by mr W last updated on 26/Jun/24

$n o n e o f t h e m .$
Commented by Tawa11 last updated on 26/Jun/24

$Thanks sir .$ $Answer should be 2052 sir ?$ $by just adding 28 to 2024 ?$
Commented by A5T last updated on 26/Jun/24

$T h e + 28 r u l e w o r k s o n l y f o r l e a p y e a r s .$
Commented by mr W last updated on 26/Jun/24

$2024 i s a l e a p y e a r . t h e n e x t y e a r$ $w i t h s a m e c a l e n d e r m u s t a l s o b e a$ $l e a p y e a r . s a y i t i s 2024 + 4 n .$ $w e h a v e n y e a r s w i t h 366 d a y s a n d$ $3 n y e a r s w i t h 365 d a y s . s u c h t h a t$ $t h a t y e a r s t a r t s w i t h t h e s a m e$ $w e e k d a y a s 2024,$ $3 n \times 365 + n \times 366 = 1461 n m u s t b e$ $d i v i s i b l e b y 7 . w e g e t n_{m i n} = 7 . t h a t$ $m e a n s a f t e r 4 \times 7 = 28 y e a r s, i . e . t h e$ $y e a r 2052 h a s t h e s a m e c a l e n d e r a s$ $2024 .$
Commented by Tawa11 last updated on 26/Jun/24

$Why 3 n years in 365 day sir$
Commented by Tawa11 last updated on 26/Jun/24

$Thanks sir . I appreciate$
Commented by mr W last updated on 26/Jun/24

$a l e a p y e a r h a s 366 d a y s, a n o r m a l$ $y e a r h a s 365 d a y s .$ $a m o n g 4 n y e a r s, t h e r e a r e n l e a p$ $y e a r s, t h e o t h e r 3 n y e a r s a r e n o r m a l$ $y e a r s .$
	Answered by A5T last updated on 26/Jun/24

	$2024 J a n u a r y - x d a y o f t h e w e e k$ $2025 ∥ - x + 2 d a y$ $2026 ∥ - x + 3$ $2027 ∥ - x + 4$ $2028 ∥ - x + 5$ $2029 ∥ - x + 7 \equiv x (m o d 7)$ $B u t 2029 i s n o t a l e a p y e a r, s o y o u c o n t i n u e$ $w i t h t h i s p r o c e s s u n t i l y o u g e t a l e a p y e a r (O n e$ $g e t s 2052) .$ $[A d d + 2 i f t h e p r e v i o u s y e a r w a s a l e a p y e a r,$ $+ 1 o t h e r w i s e] .$
	Commented by Tawa11 last updated on 26/Jun/24

	$Thanks sir, I appreciate .$
	Commented by A5T last updated on 26/Jun/24

	$I f y i s a l e a p y e a r, t h e n t h e n u m b e r o f l e a p$ $y e a r s f r o m y t o y + 4 q (e x c l u d i n g) i s q$ $x + q + 4 q \equiv x (m o d 7)$ $\Rightarrow 5 q \equiv 0 (m o d 7) \Rightarrow q \equiv 0 (m o d 7) \Rightarrow 4 q \equiv 0 (m o d 28)$ $S o, a l w a y s a d d m u l t i p l e s o f 28 t o g e t a$ $l e a p y e a r s t a r t i n g f r o m t h e s a m e d a y .$
	Commented by Tinku Tara last updated on 26/Jun/24

	$In leap years you need to also$ $consider the fact year divible by$ $100 are not leap years however$ $years divisble by 400 are leap years .$ $1900 not a leap year$ $2000 a leap year$
	Commented by A5T last updated on 26/Jun/24

	$Y e s, i f a y e a r d i v i s i b l e b y 100 b u t n o t b y 400$ $i s b e t w e e n y a n d y + 4 q, t h e n t h e n u m b e r o f$ $l e a p y e a r s f r o m y t o y + 4 q (e x c l u d i n g) i s q - 1$ $\Rightarrow x + q - 1 + 4 q \equiv x (m o d 7) \Rightarrow 5 q \equiv 1 (m o d 7)$ $\Rightarrow q \equiv 3 (m o d 7) \Rightarrow 4 q = 4 (7 k + 3) = 28 k + 12$ $S o, 12 i s t h e s m a l l e s t w e a d d i n t h a t c a s e .$
	Answered by BaliramKumar last updated on 27/Jun/24

	$\begin{array}{ccccccccc} year & Remainder & Adding \\ 2023 & \frac{23}{4} \overset{R}{=} 3 & + 11 \\ 2022 & \frac{22}{4} \overset{R}{=} 2 & + 11 \\ 2021 & \frac{21}{4} \overset{R}{=} 1 & + 6 \\ 1900 & \frac{00}{4} \overset{R}{=} 0 & \pm 6 \\ 2024 & Leap & + 28 \\ 2080 & Leap & + 40 \\ 2072 & Leap & + 40 \\ 1972 & Leap & + 28 \end{array}$
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