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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 941 · 40 questions
TalentJR

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

NameDateTime takenScore ___ / 40
  1. 1.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 135 (c) 48 (d) 15
  2. 2.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 441 (c) 451 (d) 450
  3. 3.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 228 (c) 230 (d) 238
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  5. 5.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  6. 6.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  7. 7.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 351 (c) 360 (d) 361
  8. 8.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 41 (c) 42 (d) 32
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 4 (b) 5 (c) 3 (d) 2
  10. 10.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 283 (c) 260 (d) 282
  11. 11.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  12. 12.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 398 (b) 490 (c) 480 (d) 489
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 7 (b) 16 (c) 17 (d) 18
  14. 14.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 582 (c) 591 (d) 592
  15. 15.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
  16. 16.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 603 (c) 612 (d) 613
  17. 17.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 14 (b) 4 (c) 16 (d) 15
  19. 19.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 63 (c) 7 (d) 21
  20. 20.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 372 (c) 320 (d) 373
  21. 21.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 9 (c) 30 (d) 81
  22. 22.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  23. 23.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 75 (b) 216 (c) 72 (d) 24
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 99? (a) 19 (b) 9 (c) 20 (d) 21
  25. 25.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 459 (b) 460 (c) 378 (d) 450
  26. 26.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 165 (b) 166 (c) 156 (d) 174
  27. 27.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 160 (c) 150 (d) 159
  28. 28.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 72 (c) 27 (d) 8
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 14 (b) 13 (c) 3 (d) 15
  30. 30.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 366 (c) 375 (d) 376
  31. 31.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 427 (b) 426 (c) 417 (d) 356
  32. 32.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 18 (c) 57 (d) 162
  33. 33.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 20 (b) 9 (c) 21 (d) 19
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 15 (b) 5 (c) 16 (d) 17
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 3 (b) 2 (c) 4 (d) 5
  37. 37.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 60 (c) 180 (d) 20
  38. 38.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 387 (c) 378 (d) 330
  39. 39.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 117 (c) 126 (d) 108
  40. 40.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 51 (c) 54 (d) 153

Answer key

  1. 45
  2. 450
  3. 237
  4. 5
  5. 2
  6. 5
  7. 360
  8. 41
  9. 4
  10. 282
  11. 7
  12. 489
  13. 17
  14. 591
  15. 2
  16. 612
  17. 9
  18. 15
  19. 21
  20. 372
  21. 27
  22. 9
  23. 72
  24. 20
  25. 459
  26. 165
  27. 159
  28. 24
  29. 14
  30. 375
  31. 426
  32. 54
  33. 6
  34. 20
  35. 16
  36. 4
  37. 60
  38. 387
  39. 117
  40. 51

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