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TSR Wiki > Study Help > Subjects and Revision > Mathematics > STEP > STEP I 1992 question 1 solution

• Today is June 26th 1992
• We want to know April 3rd 1905
• This was 86 years ago, plus a year and a bit more.
• Those 86 years, starting in 1905, will have 21 leap years.
• A leap year has 366 days. 366 mod7 shows this adds two days every leap year.
• A non-leap year has 365 days. 365 mod7 shows this adds one day.
• So, from 1905, we are adding 21*2 + 65*1 = 42 + 65 = 107 days.
• 107 mod7 = 2.
• So we currently have a shift of 2 day, up until April 3rd 1991.
• If June 26th 1992 was a Friday, and 1992 is a leap year, then June 26th 1991 will be a Wednesday.
• This makes June 5th 1991 a Wednesday.
• This makes June 1st 1991 a Sat.
• This makes May 31st 1991 a Friday.
• Between April 3rd and May 31st there are 27 + 31 = 58 days. 58 mod7 = 2
• So April 3rd of 1991 was a Wednesday.
• Remembering the two days shift to go back to 1905 gives us Monday

Done.

Solution by Lusus Naturae.