Worksheet Answers
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Answers to Workshop Problems UWI, Mona Campus Workshop of March 5, 2009 1) 29 2) 46, 10, 56, 11 3) 25 or 85 4)
a) 61
4)
b) 301
5) The smallest such number is 2519. Others may be produced by adding multiples of 2520. 6) 0 7) $1540. Hints: How many times will the hands be perpendicular between 8 and 10 o’clock? How many times between 2 and 4 o’clock? 8) 18 7→ 8, 49 7→ 12, and 371 7→ 10. The rule is to sum the digits and subtract 1. 9) 364. Note that all cars entering at A must leave at either B or C. 10) There are eight magic squares, as shown below. ........................................................................... ... .. ... ... ... ... . .. ... ... .......................................................................... ... ... ... ... ... ... ... .. ... .. ... ... ... . . . .......................................................................... ... .. . . .... ... ... .... ... .. ... ... .. . . . .......................................................................
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11) 3 12)
a) 8 Workshop of March 12, 2009
1) One solution is 41312432. This is not unique because, for example, the digits may be written backwards to produce 23421314. Other solutions may also exist. 2) 160 + 120π cubic metres
3) holstein 4) 25 triangles 5) The smallest such number is 2519. Others may be produced by adding multiples of 2520. 6) $1540. Hints: How many times will the hands be perpendicular between 8 and 10 o’clock? How many times between 2 and 4 o’clock? 7) 18 7→ 8, 49 7→ 12, and 371 7→ 10. The rule is to sum the digits and subtract 1. 8)
a) 8
9) 3 Workshop of March 19, 2009 This problem set was mistakenly dated March 12, 2009. In fact, it was a set of new problems discussed on March 19. 1) F = 7 2) 16 factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 3) 120◦ 4) 18, 046 5) 12 √ 6) 3/2 7) 576 8) Two: 7436 and 3476. Note that a number is divisible by 44 if and only if it is divisible both by 4 and 11. 9) Either 18 or 21 10) 180 (with n = 12 and n + 3 = 15)
a) 61
4)
b) 301
5) The smallest such number is 2519. Others may be produced by adding multiples of 2520. 6) 0 7) $1540. Hints: How many times will the hands be perpendicular between 8 and 10 o’clock? How many times between 2 and 4 o’clock? 8) 18 7→ 8, 49 7→ 12, and 371 7→ 10. The rule is to sum the digits and subtract 1. 9) 364. Note that all cars entering at A must leave at either B or C. 10) There are eight magic squares, as shown below. ........................................................................... ... .. ... ... ... ... . .. ... ... .......................................................................... ... ... ... ... ... ... ... .. ... .. ... ... ... . . . .......................................................................... ... .. . . .... ... ... .... ... .. ... ... .. . . . .......................................................................
........................................................................... ... .. ... ... ... ... . .. ... ... .......................................................................... ... ... ... ... ... ... ... .. ... .. ... ... ... . . . .......................................................................... ... .. . . .... ... ... .... ... .. ... ... .. . . . .......................................................................
....................................................................... ... ... ... ... .. .. ... ... ... ... ... . ........................................................................ .. . ... . .... ... .... .. .. .. .. .. ... ... ... . ...................................................................... ... ... ... .. ... . . . .... .... .... .. .. .. .. . .....................................................................
....................................................................... ... ... ... ... .. .. ... ... ... ... ... . ........................................................................ .. . ... . .... ... .... .. .. .. .. .. ... ... ... . ...................................................................... ... ... ... .. ... . . . .... .... .... .. .. .. .. . .....................................................................
..................................................................... ... .... .... .... ... .. .. .. ... . . . .......................................................................... .. .. .. .. ... ... ... ... .. .. .. .. ... .. .. .. . . . . .......................................................................... .. .. .. .. ... ... ... ... .. . . . .......................................................................
..................................................................... ... .... .... .... ... .. .. .. ... . . . .......................................................................... .. .. .. .. ... ... ... ... .. .. .. .. ... .. .. .. . . . . .......................................................................... .. .. .. .. ... ... ... ... .. . . . .......................................................................
............................................................................ .. ... .. .. .. .. .. ... ... . . ........................................................................... .. .. .. ... ... ... ... .... .. .. .. .. .. . . ......................................................................... ... .. .. .. ... .. .. .. ... ... ... ... .. . .. .. ......................................................................
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11) 3 12)
a) 8 Workshop of March 12, 2009
1) One solution is 41312432. This is not unique because, for example, the digits may be written backwards to produce 23421314. Other solutions may also exist. 2) 160 + 120π cubic metres
3) holstein 4) 25 triangles 5) The smallest such number is 2519. Others may be produced by adding multiples of 2520. 6) $1540. Hints: How many times will the hands be perpendicular between 8 and 10 o’clock? How many times between 2 and 4 o’clock? 7) 18 7→ 8, 49 7→ 12, and 371 7→ 10. The rule is to sum the digits and subtract 1. 8)
a) 8
9) 3 Workshop of March 19, 2009 This problem set was mistakenly dated March 12, 2009. In fact, it was a set of new problems discussed on March 19. 1) F = 7 2) 16 factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 3) 120◦ 4) 18, 046 5) 12 √ 6) 3/2 7) 576 8) Two: 7436 and 3476. Note that a number is divisible by 44 if and only if it is divisible both by 4 and 11. 9) Either 18 or 21 10) 180 (with n = 12 and n + 3 = 15)
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