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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 489 · 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 4? (a) 5 (b) 3 (c) 10 (d) 4
  2. 2.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 6 (d) 14
  3. 3.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) 180 (b) 20 (c) 60 (d) 63
  4. 4.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 11 (d) 10
  5. 5.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 11 (c) 36 (d) 33
  6. 6.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) 162 (b) 57 (c) 54 (d) 18
  7. 7.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 154 (c) 146 (d) 145
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 6 (b) 15 (c) 16 (d) 17
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 6 (b) 5 (c) 8 (d) 7
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 7 (b) 4 (c) 5 (d) 6
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 84? (a) 19 (b) 20 (c) 18 (d) 8
  12. 12.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 130 (c) 148 (d) 139
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 67? (a) 14 (b) 16 (c) 6 (d) 15
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 56? (a) 5 (b) 17 (c) 15 (d) 16
  15. 15.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) 54 (b) 153 (c) 51 (d) 17
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 19 (b) 17 (c) 7 (d) 18
  17. 17.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 338 (b) 399 (c) 390 (d) 400
  18. 18.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 330 (c) 339 (d) 340
  19. 19.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 477 (c) 468 (d) 478
  20. 20.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 188 (c) 187 (d) 196
  21. 21.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 376 (c) 457 (d) 447
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 21 (b) 19 (c) 9 (d) 20
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 9 (b) 19 (c) 18 (d) 20
  24. 24.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 258 (c) 250 (d) 267
  25. 25.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) 12 (b) 108 (c) 39 (d) 36
  26. 26.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) 48 (b) 135 (c) 15 (d) 45
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 19 (b) 17 (c) 7 (d) 18
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 17 (b) 19 (c) 7 (d) 18
  29. 29.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 384 (c) 375 (d) 385
  30. 30.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  31. 31.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 362 (b) 426 (c) 436 (d) 435
  32. 32.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 498 (c) 508 (d) 410
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 5 (b) 4 (c) 6 (d) 3
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 19 (b) 17 (c) 18 (d) 7
  35. 35.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
  36. 36.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 118 (c) 127 (d) 136
  37. 37.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 224 (c) 229 (d) 219
  38. 38.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 607 (b) 476 (c) 606 (d) 597
  39. 39.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 39 (c) 13 (d) 42
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 3 (b) 13 (c) 15 (d) 14

Answer key

  1. 4
  2. 6
  3. 60
  4. 9
  5. 33
  6. 54
  7. 145
  8. 16
  9. 7
  10. 6
  11. 19
  12. 139
  13. 15
  14. 16
  15. 51
  16. 18
  17. 399
  18. 339
  19. 477
  20. 187
  21. 456
  22. 20
  23. 19
  24. 267
  25. 36
  26. 45
  27. 18
  28. 18
  29. 384
  30. 7
  31. 435
  32. 507
  33. 5
  34. 18
  35. 5
  36. 127
  37. 228
  38. 606
  39. 39
  40. 14

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