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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 598 · 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 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) 216 (b) 75 (c) 72 (d) 24
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 19 (d) 20
  3. 3.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 553 (b) 543 (c) 552 (d) 440
  4. 4.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  5. 5.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) 63 (c) 66 (d) 21
  6. 6.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  7. 7.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 36 (c) 35 (d) 26
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 17 (b) 15 (c) 16 (d) 5
  9. 9.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  10. 10.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 186 (c) 202 (d) 195
  11. 11.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 16 (b) 51 (c) 48 (d) 144
  12. 12.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 142 (c) 124 (d) 133
  13. 13.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 10 (d) 8
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 9 (b) 7 (c) 6 (d) 8
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 18 (b) 16 (c) 17 (d) 6
  16. 16.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) 18 (b) 6 (c) 54 (d) 21
  17. 17.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 95 (b) 96 (c) 104 (d) 86
  18. 18.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  19. 19.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 4 (b) 14 (c) 13 (d) 15
  21. 21.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 53 (b) 62 (c) 44 (d) 54
  22. 22.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 36 (c) 108 (d) 12
  23. 23.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  24. 24.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  25. 25.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) 72 (b) 8 (c) 27 (d) 24
  26. 26.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 6 (d) 13
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 56? (a) 6 (b) 5 (c) 3 (d) 4
  28. 28.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 33 (c) 10 (d) 30
  29. 29.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 22 (b) 40 (c) 32 (d) 31
  30. 30.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 332 (b) 391 (c) 390 (d) 381
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 18 (b) 16 (c) 6 (d) 17
  32. 32.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 252 (c) 246 (d) 261
  33. 33.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 128 (c) 118 (d) 127
  34. 34.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 23 (c) 207 (d) 72
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 6 (b) 5 (c) 4 (d) 3
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 55? (a) 16 (b) 5 (c) 17 (d) 15
  37. 37.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 600 (c) 478 (d) 610
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 15 (b) 17 (c) 6 (d) 16
  39. 39.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  40. 40.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 208 (c) 198 (d) 207

Answer key

  1. 72
  2. 19
  3. 552
  4. 5
  5. 63
  6. 3
  7. 35
  8. 16
  9. 6
  10. 195
  11. 48
  12. 133
  13. 7
  14. 8
  15. 17
  16. 18
  17. 95
  18. 8
  19. 4
  20. 14
  21. 53
  22. 36
  23. 2
  24. 4
  25. 24
  26. 7
  27. 5
  28. 30
  29. 31
  30. 390
  31. 17
  32. 261
  33. 127
  34. 69
  35. 5
  36. 16
  37. 609
  38. 16
  39. 5
  40. 207

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