1. If you take 5 2 + 15 2 + 15 2 ... you will find that the ball is destined to approach but never touch the 15-and 30-yard lines. With each exchange of penalties it comes closer.
2. It is easy to see that with every 12 games played, you will break even if Mudville wins 5, because
Because 156 divided by 12 is 13, you must multiply the games above by 13.
In this way we can see that the Mudville Nine won 65 games.
3. Babe Ruth hit a home run every 2.57 games. Roger Maris hit a home run every 2.66 games. So Ruth was ahead, but was perhaps less fatigued from the shorter season !
Making Allowances
1. You might begin by putting 1 into your machine (rather than .01) because your calculator may drop the extra decimals without your realizing it. In any case, if you have an 8-digit calculator, and double the sum continuously, on the 27th day your display will read 67108864. If you double again you will exceed its capacity. You can get around this difficulty by taking the first four digits and doubling them the required number of times, then the last four digits, combining your answers. The amount you will earn on the 30th day is $5,368,709.12. But you still have the problem of adding. your earnings for all 30 days. Must you do this tediously, or is there a short cut? Notice that your earnings on any given day will be 1 larger than your total earnings of all the previous days. Therefore, you can take the amount earned on the 30th day, double it, and subtract 1, for an answer of $10,737,418.23.
2. Under proposition (b) you will only earn $4.65. Under proposition (c) put 1 into your machine and multiply by 1.03 continuously. On the 15th day your earnings will exceed and so will become 2, but they will never reach 3 in a month. Therefore, your earnings are:
14 days @ 1 | .14 |
16 days @ 2 | .32 |
.46 |
3. The childrens allowances are figured as follows:
Alices share would be 12.1 33.25 50.
Calculator Mathemetrics
- About 183 cm.
- About 175 cm.
- About 91 kg.
- About 10.94 seconds.
- A mile equals about 1,600 meters, but a more likely choice is to use a round number, in this case 1,500.
- About 3 minutes 44 seconds.
- About 88.5 k.p.h.
- 70metric wont help your golf score, unless the length of the holes is changed.
- Assuming the size of the diamond alone is changed, not the ballpark itself, the change would have little effect on home runs. Most are hit out of the park and, while it would be slightly harder to make home runs inside the park, these are quite rare.
- It would be dangerous to assume that because of the slightly longer distance his successes would fall off in the same proportion. Maybe 50 yards represents the limit of his ability, and 50 meters (about 55 yards) would be too much and he would never make them.
- The Indianapolis 805 (kilometers, approximately).
- About 28 square meters.
- About 198,000 cubic meters.
- Around kilograms, priced at about 95.
- Almost meters.
- Almost meters.
- About kilograms, allowing for a slight fish story.
- About 9.3 cents per kilometer.
- About 580 kilometers per hour.
- About 15.3, rounding off in your favor, as you might hope.
- 40 degrees.
- 160 degrees Fahrenheit equals 320 degrees Centigrade.
- 12.3 degrees Fahrenheit equals24.6 degrees Ceriti-grade, approximately.
Treasure Hunt
- DOORBELL
- 3507 = CLOSET
- 708451 = FISHBOWL
- 114 = HI-FI
- 700500 = FOOTSTOOL
- 771501 = WINDOWSILL
- 371800 = AUTOMOBILE
- 407378 = TABLECLOTH
- 3807 = GLOBE
- 378330 = COFFEE TABLE
- 53557 = GLASSES
- 345451 = DISHWASHER
- 35008 = BOOKCASE
- 45105 = SOAPDISH
- 5571007 = LOOKING GLASS
The Root of the Matter
1. The square root of (1.5 x 800) comes to about 34.64 miles. Can you see why this formula would not work on the moon?
2. 52 122 = 132.
3. About 12.49 feet.
4. If you think of the diamond as four right triangles butted together as shown above, you can easily find the distance to the center of the field. By taking the square root of 4050 (902 2) you find that the center of the field is about 63.64 feet from all bases, and so the pitcher stands closer to home plate.
Strictly for Squares
- If you have an eight-digit calculator, 27 times.
- Your answer would tend towards 0.
- Your answer would tend towards 1.
- Your answer would tend towards 1.
More Upside-Down Displays
- ISLE
- BLISS
- BILLS
- HEEL, SOLE
- HE SOBS
- BLESSES
- BIBLE
- HOSE
- ILL
- SHE LIES
- BOIL
- EBBS
- BEES
- HOBBIES
Family Finances
1. Let us say that the daily paper weighs 1 quiblon, and the Sunday paper weighs 4 quiblons. The daily papers in a week weigh 6 quiblons, plus a 25 % bonus means you will get credit for 7.5 quiblons. The total weight for the week comes to 11.5 quiblons, of which 4 applies to Sunday. 4 11.5 $1 gives 34.78 of your tip which applies to the Sunday paper. Your sisters weekly paper weighs as much as the Sunday paper, and since no bonus applies to Sunday, she should receive as much as your Sunday tip, or 2.17. Of course she should thank him, for politeness never costs anything, and if he actually gave her 3 she should thank him warmly for his generosity.
2. Plan A is substantially better. The following table shows how much:
Shopping Spree
A. The second is cheaper by $.0004167 per ounce 48 | Savings 2 |
B. The first is cheaper by $.0011072 per ounce, 168 | Savings 19 |