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This week, spring is in the air.

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Time of Day

Pretend you are in New York during daylight on the vernal equinox. You note your watch’s second hand is on a minute mark and exactly 18 minute marks ahead of the hour hand.

What time is it?

The Missing Element

The open-ended sequence …35, 45, 60, q, 120, 180, 280, 450, 744, 1260… has an undisclosed element, q.

Find a simple continuous function to generate the sequence and compute the surprise answer for q.

Solutions to week 131

In Knight Trap, the knight can be trapped in 15 moves. In My Number is 136, Ana has 135 on her forehead and Boris has 136 on his.

The knight can be trapped in 15 moves as shown in the figure.

My Number is 136 answer explained:
a = 1 and b = 135. Ana sees 136 on Boris and knows whatever product Boris sees (1 × 135, 2 × 134, 3 × 133, etc.), he can’t know his number. Boris sees 135 on Ana and considers he may have 3 + 45 (= 47 + 1), 5 + 27 (= 31 + 1), 9 + 15 (= 23 + 1), or 1 + 135. The first three possibilities are eliminated by adding to one more than a prime (which would disallow Ana from making her statement) so Boris deduces his number is 136.

Recent Weeks

Links to all of the puzzles and solutions are on the Complete Varsity Math page.

Come back next week for answers and more puzzles.