Fourth Advent and Christmas Eve
Number Theory
Level
4
This year, in 2017, the fourth Advent (the fourth Sunday of the month) and Christmas Eve fell on the same day.
The next time this will happen again is in 2023.
But how often does this occur on average?
every 5 years
every 6 years
every 7 years
every 8 years
every 14 years
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1 solution
here is a program on Mathematica that searches the next 1000 years
Select[Range[2017,3017],DayName[DateObject[{#,12,24}]]==Sunday&]here are the results
{2017,2023,2028,2034,2045,2051,2056,2062,2073,2079,2084,2090,2102,2113,2119,2124,2130,2141,2147,2152,2158,2169,2175,2180,2186,2197,2209,2215,2220,2226,2237,2243,2248,2254,2265,2271,2276,2282,2293,2299,2305,2311,2316,2322,2333,2339,2344,2350,2361,2367,2372,2378,2389,2395,2400,2406,2417,2423,2428,2434,2445,2451,2456,2462,2473,2479,2484,2490,2502,2513,2519,2524,2530,2541,2547,2552,2558,2569,2575,2580,2586,2597,2609,2615,2620,2626,2637,2643,2648,2654,2665,2671,2676,2682,2693,2699,2705,2711,2716,2722,2733,2739,2744,2750,2761,2767,2772,2778,2789,2795,2800,2806,2817,2823,2828,2834,2845,2851,2856,2862,2873,2879,2884,2890,2902,2913,2919,2924,2930,2941,2947,2952,2958,2969,2975,2980,2986,2997,3009,3015}let's have a look at the differences
{6,5,6,11,6,5,6,11,6,5,6,12,11,6,5,6,11,6,5,6,11,6,5,6,11,12,6,5,6,11,6,5,6,11,6,5,6,11,6,6,6,5,6,11,6,5,6,11,6,5,6,11,6,5,6,11,6,5,6,11,6,5,6,11,6,5,6,12,11,6,5,6,11,6,5,6,11,6,5,6,11,12,6,5,6,11,6,5,6,11,6,5,6,11,6,6,6,5,6,11,6,5,6,11,6,5,6,11,6,5,6,11,6,5,6,11,6,5,6,11,6,5,6,12,11,6,5,6,11,6,5,6,11,6,5,6,11,12,6}here is the program that returns the answer
N@Mean@Differences@Select[Range[2017,3017],DayName[DateObject[{#,12,24}]]==Sunday&]7.17986