# 1. Problem Description

A factory produces small electronic devices that each contain an identical image classifier. The classifier is a lightweight convolutional network trained to recognize handwritten digits (0 through 9). Due to hardware constraints, each device can only receive a single training example over its update channel before retraining.

Your job is to design that single training example.

You will craft:
- one **28×28 grayscale image**
- one **10-dimensional soft label vector**

A fixed CNN will then be retrained from scratch using only your example and evaluated on real handwritten digits. The better your synthetic example encodes information about all ten digit classes, the higher the model scores.

---

# 2. Dataset

```text
data/
├── mnist_images/
│   ├── img_00000.png
│   ├── img_00001.png
│   ├── ...
│   └── img_59999.png
└── train_labels.csv
```

The training set is provided for your analysis only. Your submission contains no real images. The hidden test set is drawn from the same distribution.

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# 3. Task

Produce exactly **one synthetic training sample** consisting of:

- A **28×28 grayscale image**
  - 784 pixel values
  - floats in `[0, 1]`

- A **10-dimensional soft label vector**
  - non-negative values
  - sums to `1.0`