Slap in the face

Problem 199 — What you see is isn’t always what you see, as this month’s problem by Richard Keck of Wadsworth, Ohio, demonstrates.

It was a warm, sunny Saturday afternoon, and the Corner Church of Tooterville’s annual picnic was well underway. Two board members were lazily watching a helicopter zoom directly overhead.

It was well known that these two could never agree on anything. George Mc- Groundbound remarked that it was interesting that part of the main rotor appeared to be standing still while the chopper flew directly overhead.

“I always though you needed glasses!” retorted Sim Skylark. “You couldn’t have seen any such thing.”

The helicopter has a two-bladed (as opposed to a four-bladed) main rotor with a 30-ft diameter. Both George and Sim heard eight “slaps” per second as it passed overhead. The chopper was cruising at 150 knots.

What part of the rotor, if any, looked like it was standing still?

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Solution to last month’s problem 198 — You examine all the possibilities if you answered 72, 18, and 1. Here’s the right combination:

We don’t know Blabb’s house number as McBean did, so we must write down all the triplets of numbers whose product is 1,296. Unfortunately there are 42 of them:

1, 296 + 1 + 1 = 1, 298
648 + 2 + 1 = 651
432 + 3 + 1 = 436
324 + 4 + 1 = 329
324 + 2 + 2 = 328
216 + 6 + 1 = 223
216 + 3 + 2 = 221
162 + 8 + 1 = 171
162 + 4 + 2 = 168
144 + 9 + 1 = 154
144 + 3 + 3 = 150
108 + 12 + 1 = 121
108 + 6 + 2 = 116
108 + 4 + 3 = 115
81 + 16 + 1 = 98
81+ 8 + 2 = 91
81 + 4 + 4 = 89
72 + 18 + 1 = 91
72 + 9 + 2 = 83
72 + 6 + 3 = 81
54 + 24 + 1 = 79
54 + 8 + 3 = 54
54 + 6 + 4 = 64
54 + 12 + 2 = 68
48 + 27 + 1 = 76
48 + 9 + 3 = 60
36 + 36 + 1 = 73
36 + 6 + 6 = 48
36 + 9 + 4 = 49
36 + 18 + 2 = 56
36 + 12 + 3 = 51
27 + 12 + 4 = 43
27 + 24 + 2 = 53
27 + 8 + 6 = 41
27 + 16 + 3 = 46
24 + 9 + 6 = 39
24 + 18 + 3 = 45
18 + 18 + 4 = 40
18 + 12 + 6 = 36
18 + 9 + 8 = 35
16 + 9 + 9 = 34
12 + 12 + 9 = 33

Even though McBean knew Blabb’s address, he had to make a phone call to get more information. Therefore the house number was 91, because this is the only number that is the sum of more than one combination. Blabb was incensed at being called an octogenarian, so his age must have been 72.

The correct combination is 72, 18, and 1. McBean began to wonder if he should consider a career in law.