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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 66 · 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.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 80? (a) 18 (b) 19 (c) 17 (d) 8
  3. 3.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) 108 (b) 12 (c) 36 (d) 39
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 4 (b) 2 (c) 3 (d) 1
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 4 (b) 5 (c) 2 (d) 3
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 16 (b) 15 (c) 17 (d) 6
  7. 7.The numbers 1 to 9 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) 5 (c) 15 (d) 18
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 18 (b) 8 (c) 20 (d) 19
  9. 9.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  11. 11.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 268 (c) 295 (d) 285
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 8 (b) 5 (c) 6 (d) 7
  13. 13.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 630 (b) 498 (c) 639 (d) 640
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 88? (a) 18 (b) 17 (c) 8 (d) 19
  15. 15.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 435 (c) 362 (d) 436
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 20 (b) 9 (c) 21 (d) 19
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 64? (a) 17 (b) 6 (c) 16 (d) 15
  18. 18.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 141 (b) 150 (c) 142 (d) 132
  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) 135 (b) 48 (c) 15 (d) 45
  20. 20.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 600 (b) 472 (c) 591 (d) 601
  21. 21.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  22. 22.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
  23. 23.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 364 (c) 363 (d) 314
  24. 24.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) 144 (c) 51 (d) 48
  25. 25.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 628 (b) 490 (c) 627 (d) 618
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 17 (b) 16 (c) 6 (d) 18
  27. 27.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 358 (c) 420 (d) 429
  28. 28.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 4 (d) 2
  29. 29.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) 72 (c) 24 (d) 75
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 13 (b) 15 (c) 14 (d) 4
  31. 31.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) 23 (b) 72 (c) 207 (d) 69
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 14 (b) 13 (c) 3 (d) 15
  33. 33.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 211 (c) 201 (d) 212
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 7 (b) 9 (c) 6 (d) 8
  35. 35.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
  36. 36.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) 54 (c) 21 (d) 18
  37. 37.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 188 (c) 179 (d) 180
  38. 38.The numbers 18 to 26 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) 66 (c) 22 (d) 198
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 77? (a) 17 (b) 7 (c) 19 (d) 18
  40. 40.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 276 (c) 262 (d) 286

Answer key

  1. 5
  2. 18
  3. 36
  4. 3
  5. 4
  6. 16
  7. 15
  8. 19
  9. 4
  10. 3
  11. 294
  12. 7
  13. 639
  14. 18
  15. 435
  16. 20
  17. 16
  18. 141
  19. 45
  20. 600
  21. 2
  22. 24
  23. 363
  24. 48
  25. 627
  26. 17
  27. 429
  28. 3
  29. 72
  30. 14
  31. 69
  32. 14
  33. 210
  34. 8
  35. 5
  36. 18
  37. 179
  38. 66
  39. 18
  40. 285

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