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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 832 · 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.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 99 (b) 100 (c) 108 (d) 90
  2. 2.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) 20 (c) 60 (d) 180
  3. 3.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) 21 (b) 24 (c) 7 (d) 63
  4. 4.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 119 (c) 128 (d) 120
  5. 5.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 592 (b) 591 (c) 582 (d) 466
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 19 (b) 17 (c) 18 (d) 8
  7. 7.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 5 (d) 7
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 17 (b) 5 (c) 16 (d) 15
  9. 9.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 54? (a) 16 (b) 15 (c) 17 (d) 5
  11. 11.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 433 (b) 432 (c) 423 (d) 360
  12. 12.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 15 (b) 5 (c) 17 (d) 16
  14. 14.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  15. 15.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  16. 16.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
  17. 17.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 10 (d) 6
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 7 (b) 18 (c) 17 (d) 16
  19. 19.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) 15 (b) 45 (c) 135 (d) 48
  20. 20.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 189 (b) 66 (c) 63 (d) 21
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 19 (b) 9 (c) 18 (d) 20
  22. 22.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 540 (b) 549 (c) 438 (d) 550
  23. 23.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) 81 (d) 30
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 9 (b) 8 (c) 7 (d) 6
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 5 (b) 3 (c) 6 (d) 4
  26. 26.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 138 (c) 137 (d) 146
  27. 27.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) 24 (b) 72 (c) 216 (d) 75
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 56? (a) 7 (b) 6 (c) 4 (d) 5
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 5 (b) 4 (c) 3 (d) 2
  30. 30.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 333 (c) 343 (d) 300
  31. 31.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 211 (b) 212 (c) 210 (d) 201
  32. 32.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 327 (c) 318 (d) 290
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 52? (a) 6 (b) 4 (c) 3 (d) 5
  34. 34.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 8 (d) 9
  35. 35.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 338 (c) 399 (d) 390
  36. 36.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 392 (b) 481 (c) 480 (d) 471
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 4 (b) 3 (c) 2 (d) 1
  38. 38.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 6 (b) 21 (c) 54 (d) 18
  39. 39.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 94 (c) 93 (d) 84
  40. 40.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 315 (c) 316 (d) 282

Answer key

  1. 99
  2. 60
  3. 21
  4. 119
  5. 591
  6. 18
  7. 6
  8. 16
  9. 3
  10. 16
  11. 432
  12. 4
  13. 16
  14. 5
  15. 9
  16. 9
  17. 7
  18. 17
  19. 45
  20. 63
  21. 19
  22. 549
  23. 27
  24. 8
  25. 5
  26. 137
  27. 72
  28. 6
  29. 4
  30. 342
  31. 210
  32. 327
  33. 5
  34. 8
  35. 399
  36. 480
  37. 3
  38. 18
  39. 93
  40. 315

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