Here’s this week’s Micro Softy. The solution to last week’s puzzler is below:

Timmy Johnson, a thirteen-year-old, was cruising with his dad in their classic 1957 Chevy. As they pulled up to a traffic light, a sleek 1968 Mustang rolled up beside them. Both drivers revved their engines, an unspoken challenge hanging in the air—when the light turned green, it would be a race.

The moment the light changed to green, both cars roared forward, tires screeching as they peeled off the line. But in an instant, the thrill turned to tragedy. A 2024 Mitsubishi Mirage, attempting to beat a yellow light that had already turned red, T-boned the driver’s side of the car Timmy was riding in. The impact was devastating—Timmy’s father was killed instantly.

Timmy, critically injured, was rushed to the hospital. The emergency team worked quickly, determining that he needed immediate surgery. After being prepped and placed under anesthesia, Timmy was rolled into the operating room. Moments later, the surgeon walked in, glanced at the boy, and froze.

“I can’t operate on this boy. He’s my son.”

What’s the resolution to this paradox? It is a conventional family and there are no adoptions. Solution next Monday.

Solution to Monday Micro Softy 21:  Finding More the Deadly Fentanyl Pills

Here’s a recap of last week’s difficult Micro Softy:

As a drug enforcement officer, you have 10 bottles of pills, each containing about 2,000 pills. Some of those bottles have pills laced with a deadly dose of fentanyl. The fentanyl-laced pills weigh 1.1 grams each, while the regular pills weigh exactly 1 gram. Other than their weight, the two types of pills look and feel identical. You have access to a high-tech scale that precisely measures weight. But it is expensive to use so the department insists that you minimize weighings. Your task is to identify all of the bottles containing bad pills, using the scale only once.

Here’s the solution: You take one pill out of bottle #1, two out of bottle #2, four from bottle #3, eight from bottle #4 etc. Each time, the number of pills is doubled so the 10^th bottle contributes 512 pills to the stack. The total number of pills pulled from all the bottles is 1023. All of the pills are weighed together.

To see what the weight would tell you, first assume that no pills were bad. Then the scale would read exactly 1023 grams for 1023 pills. If only bottles #2 and #3 contain bad pills, we have 2 bad pills from bottle #2 and 4 bad pills from bottle #3. The scale would then read 1023.6 grams. The only way to get the extra weight of 6 is to add 2 and 4 which points to bottles #2 and #3 as holding the bad pills. 

If you know binary numbers, you know that the ten-bit binary number

0000000110

translates to 6.  When read backwards (right to left), this corresponds to bottles #2 and #3.

This can be generalized to any combination of bottles. For example, the ten-bit binary number

1000000111

corresponds to the number 519 = 512+4+2+1. If the weighing of all pills was 1023.519 grams, we would conclude, reading backwards, that bottles #1, 2, 3 and 10 all contain bad pills.

So hurray for binary numbers!

Links to all the Micro Softies

Here’s Monday Micro Softy 21: Finding More of the Deadly Fentanyl Pills. There, you will also find links to Microsofties 11 through 20 as well.

and

At Monday Micro Softy 11: What Happened to That Other Dollar?, you will find links to the first ten Micro Softies. Have fun!