Problem 22 · 2025 Math Kangaroo
Stretch
Logic & Word Problems
clock-calendarsum-constraint
The calendar shows the days of a month, with the columns running Monday, Tuesday, …, Sunday, but the dates are missing. The two dark grey boxes are a Thursday and a Wednesday. If you add the two dates in the dark grey boxes, you get 29. What day of the week is the 1st of the month?
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Answer: D — Thursday
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Hint 1 of 3
Count the days from the grey Thursday box down to the grey Wednesday box - it is exactly 13 days later.
Still stuck? Show hint 2 →
Hint 2 of 3
So the two grey dates are 13 apart and add up to 29; find two such numbers.
Still stuck? Show hint 3 →
Hint 3 of 3
Once you know the grey Thursday's date, count back by 7s to reach the 1st.
Show solution
Approach: use the 13-day gap and the sum of 29, then walk back to the 1st
- Going down two rows and one box to the left, the grey Wednesday lands 13 days after the grey Thursday.
- Take away those extra 13 days from the sum 29, and 16 is left for two equal Thursday dates, so each is 16 ÷ 2 = 8 - the grey Thursday is the 8th.
- Counting back a week, the 1st of the month is also a Thursday (8, then 1).
- So the 1st is a Thursday, option D.
Mark:
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